(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1746318, 25760]*) (*NotebookOutlinePosition[ 1746952, 25782]*) (* CellTagsIndexPosition[ 1746908, 25778]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Finiteness for Relative Equilibria of the Four-Body Problem", "Title"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["\<\ This notebook contains computational algorithms and results which support the \ paper \"Finiteness of relative equilibria of the four-body problem\" by \ Marshall Hampton and Richard Moeckel. The notebook is divided into sections \ explaining the different kinds of computations used to verify the results in \ the paper. The reader can go through the notebook section by section, \ executing the cells in order to check the computations. Some computations were done with the other programs such as Porta, Macaulay2, \ lrs and Mixvol. As explained below, these results have simply been copied \ into this notebook so that further computations based on them can be \ illustrated.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Equations for Relative Equilibria", "Section"], Cell["\<\ First we define some functions to automatically construct the \ Albouy-Chenciner equations for central configurations. For the four-body \ problem, there are six equations for the six mutual distances.\ \>", "Text"], Cell[BoxData[{ \( (*\ Define\ mutual\ distances\ and\ normalized\ variables\ Sij\ *) \ \[IndentingNewLine]r[i_, i_] := 0\), "\[IndentingNewLine]", \(r[i_, j_] := r[j, i] /; j < i\), "\[IndentingNewLine]", \(S[i_, i_] := \ 0\), "\[IndentingNewLine]", \(S[i_, j_]\ := \(\(1/r[i, j]^3 - 1\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\( (*\ Carry\ out\ the\ sum\ in\ equation\ \((10)\)\ of\ section\ 2.1\ *) \)\ \)\), "\[IndentingNewLine]", \(\(\(P[i_, j_, n_]\ := Plus @@ Table[ m[k]*\((S[i, k]*\((r[j, k]^2 - r[i, k]^2 - r[i, j]^2)\) + S[j, k]*\((r[i, k]^2 - r[j, k]^2 - r[i, j]^2)\))\), {k, 1, n}]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\) (*\ Make\ a\ table\ of\ all\ of\ the\ Albouy - Chenciner\ equations\ and\ clear\ the\ denominators\ *) \ \), "\ \[IndentingNewLine]", \(ACeqs[ n_]\ := \ \(\(Table[P[i, j, n], {j, 2, n}, {i, 1, j - 1}] // Flatten\) // Factor\) // Numerator\)}], "Input"], Cell["\<\ Here are the equations written out with the array variables replaced by \ ordinary ones. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(varsub\ = \ {r[1, 2] \[Rule] r12, r[1, 3] \[Rule] r13, r[2, 3] \[Rule] r23, r[1, 4] \[Rule] r14, r[2, 4] \[Rule] r24, r[3, 4] \[Rule] r34, m[1] \[Rule] m1, m[2] \[Rule] m2, m[3] \[Rule] m3, m[4] \[Rule] m4};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(aceqs\ = \ ACeqs[4] /. varsub\)}], "Input"], Cell[BoxData[ \({\(-m4\)\ r12\^3\ r13\^3\ r14\^3\ r23\^3 + m4\ r12\ r13\^3\ r14\^5\ r23\^3 - m4\ r12\ r13\^3\ r14\^3\ r23\^3\ r24\^2 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 + m3\ r12\ r13\^5\ r14\^3\ r24\^3 - m3\ r12\ r13\^3\ r14\^3\ r23\^2\ r24\^3 - m4\ r12\^3\ r13\^3\ r23\^3\ r24\^3 - m4\ r12\ r13\^3\ r14\^2\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\ r13\^2\ r14\^3\ r23\^3\ r24\^3 - 2\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3 - 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m3\ r12\ r14\^3\ r23\^5\ r24\^3 + m4\ r12\ r13\^3\ r23\^3\ r24\^5, \(-m4\)\ r12\^3\ r13\^3\ r14\^3\ r23\ \^3 + m4\ r12\^3\ r13\ r14\^5\ r23\^3 - m4\ r12\^3\ r13\ r14\^3\ r23\^3\ r34\^2 + m2\ r12\^5\ r13\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\ r14\^3\ r23\^2\ r34\^3 - m4\ r12\^3\ r13\^3\ r23\^3\ r34\^3 - m4\ r12\^3\ r13\ r14\^2\ r23\^3\ r34\^3 - 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r12\^2\ r13\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r23\^3\ r34\^3 + m2\ r13\ r14\^3\ r23\^5\ r34\^3 + m4\ r12\^3\ r13\ r23\^3\ r34\^5, \(-m4\)\ r12\^3\ r13\^3\ r23\^3\ r24\ \^3 + m4\ r12\^3\ r13\^3\ r23\ r24\^5 - m4\ r12\^3\ r13\^3\ r23\ r24\^3\ r34\^2 - m4\ r12\^3\ r13\^3\ r23\^3\ r34\^3 - m4\ r12\^3\ r13\^3\ r23\ r24\^2\ r34\^3 - 2\ m2\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m3\ r12\^3\ r13\^3\ r24\^3\ r34\^3 + m1\ r12\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r13\^2\ r23\ r24\^3\ r34\^3 - m1\ r12\^2\ r13\^3\ r23\ r24\^3\ r34\^3 + m1\ r13\^5\ r23\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r23\^3\ r24\^3\ r34\^3 + m4\ r12\^3\ r13\^3\ r23\ r34\^5, m3\ r12\^3\ r13\^5\ r14\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3 - m3\ r12\^3\ r13\^3\ r14\ r24\^3\ r34\^2 + m2\ r12\^5\ r13\^3\ r14\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\^3\ r34\^3 - m2\ r12\^3\ r13\^3\ r14\ r24\^2\ r34\^3 - 2\ m1\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - 2\ m4\ r12\^3\ r13\^3\ r24\^3\ r34\^3 - m3\ r12\^3\ r13\^2\ r14\ r24\^3\ r34\^3 - m2\ r12\^2\ r13\^3\ r14\ r24\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r13\^3\ r14\^3\ r24\^3\ r34\^3 + m2\ r13\^3\ r14\ r24\^5\ r34\^3 + m3\ r12\^3\ r14\ r24\^3\ r34\^5, m3\ r12\^3\ r14\^3\ r23\^5\ r24 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3 - m3\ r12\^3\ r14\^3\ r23\^3\ r24\ r34\^2 - 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - 2\ m4\ r12\^3\ r14\^3\ r23\^3\ r34\^3 - m3\ r12\^3\ r14\^3\ r23\^2\ r24\ r34\^3 + m1\ r12\^5\ r23\^3\ r24\ r34\^3 - m1\ r12\^3\ r14\^2\ r23\^3\ r24\ r34\^3 - m1\ r12\^2\ r14\^3\ r23\^3\ r24\ r34\^3 + m1\ r14\^5\ r23\^3\ r24\ r34\^3 - m3\ r12\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r12\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r12\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + m3\ r12\^3\ r14\^3\ r24\ r34\^5, \(-2\)\ m3\ r13\^3\ r14\^3\ r23\^3\ \ r24\^3 - 2\ m4\ r13\^3\ r14\^3\ r23\^3\ r24\^3 + m2\ r13\^3\ r14\^3\ r23\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r24\^2\ r34 - m2\ r13\^3\ r14\^3\ r23\^2\ r24\^3\ r34 + m1\ r13\^5\ r23\^3\ r24\^3\ r34 - m1\ r13\^3\ r14\^2\ r23\^3\ r24\^3\ r34 - m1\ r13\^2\ r14\^3\ r23\^3\ r24\^3\ r34 + m1\ r14\^5\ r23\^3\ r24\^3\ r34 + m2\ r13\^3\ r14\^3\ r24\^5\ r34 - m2\ r13\^3\ r14\^3\ r23\^3\ r34\^3 - m2\ r13\^3\ r14\^3\ r24\^3\ r34\^3 - m1\ r13\^3\ r23\^3\ r24\^3\ r34\^3 - m1\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m1\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m2\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m3\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3 + 2\ m4\ r13\^3\ r14\^3\ r23\^3\ r24\^3\ r34\^3}\)], "Output"] }, Open ]], Cell["Next we enter in the three Dziobek equations.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Equations\ \((12)\)\ from\ section\ 2.2\ \ *) \)\(\[IndentingNewLine]\)\(dzeqs\ = \ \({S[1, 2] S[3, 4] - S[1, 4] S[2, 3], S[1, 2] S[3, 4] - S[1, 3] S[2, 4], S[1, 3] S[2, 4] - S[1, 4] S[2, 3]} /. varsub // Factor\) // Numerator\)\)\)], "Input"], Cell[BoxData[ \({r14\^3\ r23\^3 - r12\^3\ r14\^3\ r23\^3 - r12\^3\ r34\^3 + r12\^3\ r14\^3\ r34\^3 + r12\^3\ r23\^3\ r34\^3 - r14\^3\ r23\^3\ r34\^3, r13\^3\ r24\^3 - r12\^3\ r13\^3\ r24\^3 - r12\^3\ r34\^3 + r12\^3\ r13\^3\ r34\^3 + r12\^3\ r24\^3\ r34\^3 - r13\^3\ r24\^3\ r34\^3, r14\^3\ r23\^3 - r13\^3\ r14\^3\ r23\^3 - r13\^3\ r24\^3 + r13\^3\ r14\^3\ r24\^3 + r13\^3\ r23\^3\ r24\^3 - r14\^3\ r23\^3\ r24\^3}\)], "Output"] }, Open ]], Cell["\<\ Our main system consists of these nine equations for the six mutual \ distances. \ \>", "Text"], Cell[BoxData[ \(\(acdzeqs\ = \ aceqs~Join~dzeqs;\)\)], "Input"], Cell["\<\ For constructing the upper bound we also use another system of 10 equations \ and 10 unknowns. We begin by entering the system of 11 equations and \ unknowns (13) from section 2.2 The first five are geometrical equations \ arising from the \"Cayley-Menger\" matrix of squared mutual distances. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(CM = \ {{0, 1, 1, 1, 1}, \[IndentingNewLine]{1, 0, r12^2, r13^2, r14^2}, \[IndentingNewLine]{1, r12^2, 0, r23^2, r24^2}, \[IndentingNewLine]{1, r13^2, r23^2, 0, r34^2}, \[IndentingNewLine]{1, r14^2, r24^2, r34^2, 0}};\)\), "\[IndentingNewLine]", \(geomeqs\ = \ CM . {k, m1*z1, m2*z2, m3*z3, m4*z4}\)}], "Input"], Cell[BoxData[ \({m1\ z1 + m2\ z2 + m3\ z3 + m4\ z4, k + m2\ r12\^2\ z2 + m3\ r13\^2\ z3 + m4\ r14\^2\ z4, k + m1\ r12\^2\ z1 + m3\ r23\^2\ z3 + m4\ r24\^2\ z4, k + m1\ r13\^2\ z1 + m2\ r23\^2\ z2 + m4\ r34\^2\ z4, k + m1\ r14\^2\ z1 + m2\ r24\^2\ z2 + m3\ r34\^2\ z3}\)], "Output"] }, Open ]], Cell["The other six are essentially due to Dziobek.", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(moredzeqs\ = \ \(\(Table[ S[i, j] - z[i]*z[j], {j, 2, 4}, {i, 1, j - 1}] // Flatten\) // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(\(varsub2\ = \ {z[1] \[Rule] z1, z[2] \[Rule] z2, z[3] \[Rule] z3, z[4] \[Rule] z4};\)\), "\[IndentingNewLine]", \(moredzeqs\ = \ \(moredzeqs /. varsub\) /. varsub2\)}], "Input"], Cell[BoxData[ \({1 - r12\^3 - r12\^3\ z1\ z2, 1 - r13\^3 - r13\^3\ z1\ z3, 1 - r23\^3 - r23\^3\ z2\ z3, 1 - r14\^3 - r14\^3\ z1\ z4, 1 - r24\^3 - r24\^3\ z2\ z4, 1 - r34\^3 - r34\^3\ z3\ z4}\)], "Output"] }, Open ]], Cell["\<\ The system of 10 equations and ten unknowns is obtained by eliminating k. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(geomeqsnok\ = \ {geomeqs[\([1]\)], geomeqs[\([2]\)] - geomeqs[\([5]\)], geomeqs[\([3]\)] - geomeqs[\([5]\)], geomeqs[\([4]\)] - geomeqs[\([5]\)]};\)\), "\[IndentingNewLine]", \(teneqs\ = \ geomeqsnok~Join~moredzeqs\)}], "Input"], Cell[BoxData[ \({m1\ z1 + m2\ z2 + m3\ z3 + m4\ z4, \(-m1\)\ r14\^2\ z1 + m2\ r12\^2\ z2 - m2\ r24\^2\ z2 + m3\ r13\^2\ z3 - m3\ r34\^2\ z3 + m4\ r14\^2\ z4, m1\ r12\^2\ z1 - m1\ r14\^2\ z1 - m2\ r24\^2\ z2 + m3\ r23\^2\ z3 - m3\ r34\^2\ z3 + m4\ r24\^2\ z4, m1\ r13\^2\ z1 - m1\ r14\^2\ z1 + m2\ r23\^2\ z2 - m2\ r24\^2\ z2 - m3\ r34\^2\ z3 + m4\ r34\^2\ z4, 1 - r12\^3 - r12\^3\ z1\ z2, 1 - r13\^3 - r13\^3\ z1\ z3, 1 - r23\^3 - r23\^3\ z2\ z3, 1 - r14\^3 - r14\^3\ z1\ z4, 1 - r24\^3 - r24\^3\ z2\ z4, 1 - r34\^3 - r34\^3\ z3\ z4}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Newton Polytopes", "Section"], Cell[TextData[{ "In this section we find show the ", StyleBox["Mathematica", FontSlant->"Italic"], " functions used to compute the Newton polytopes of our equations and their \ Minkowski sums. The ", StyleBox["Mathematica", FontSlant->"Italic"], " part just involves reading off all the exponent vectors and adding them. \ For the real work of finding the convex hulls we used Porta 1.3.2. The \ final result was verified using lrs 4.1." }], "Text"], Cell[CellGroupData[{ Cell["Exponent Lists", "Subsection"], Cell[TextData[{ "First we have some simple functions based on ", StyleBox["Mathematica's ", FontSlant->"Italic"], StyleBox["built-in Exponent command. Essentially a polynomial which has \ been completely expanded is represented in ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox[" as a list of its terms (with a \"Head\" of \"Plus\" in front). \ We also make use of a list of the variables whose exponents we want to read \ off. The first function below is intended to act on a single term of a \ polynomials. It applies ", FontVariations->{"CompatibilityType"->0}], StyleBox["Mathematica", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox["'s Exponent command to the monomial for each variable in the \ variable list thereby producing a list of the exponents for all the \ variables. For a polynomial, we just to this for every term to get a list of \ lists of exponents. The Union command eliminates redundancies arising from \ terms which involve the same powers of the variables with different \ coefficients.", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[{ \(GetExponents[mon_, vars_]\ := \ Map[Exponent[mon, #] &, vars]\), "\[IndentingNewLine]", \(GetAllExponents[poly_, vars_] := \[IndentingNewLine]Table[ GetExponents[poly[\([i]\)], vars], {i, 1, Length[poly]}] // Union\)}], "Input"], Cell["\<\ Here is the exponent list for the Albouy-Chenciner-Dziobek system. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(vars4bp\ = \ {r12, r13, r14, r23, r24, r34};\)\), "\[IndentingNewLine]", \(explist9\ = \ Map[GetAllExponents[#, vars4bp] &, acdzeqs]\)}], "Input"], Cell[BoxData[ \({{{0, 3, 3, 3, 3, 0}, {1, 0, 3, 5, 3, 0}, {1, 2, 3, 3, 3, 0}, {1, 3, 0, 3, 5, 0}, {1, 3, 2, 3, 3, 0}, {1, 3, 3, 2, 3, 0}, {1, 3, 3, 3, 2, 0}, {1, 3, 5, 3, 0, 0}, {1, 5, 3, 0, 3, 0}, {3, 0, 3, 3, 3, 0}, {3, 3, 0, 3, 3, 0}, {3, 3, 3, 0, 3, 0}, {3, 3, 3, 3, 0, 0}, {3, 3, 3, 3, 3, 0}}, {{0, 1, 3, 5, 0, 3}, {0, 3, 3, 3, 0, 3}, {2, 1, 3, 3, 0, 3}, {3, 0, 3, 3, 0, 3}, {3, 1, 0, 3, 0, 5}, {3, 1, 2, 3, 0, 3}, {3, 1, 3, 2, 0, 3}, {3, 1, 3, 3, 0, 2}, {3, 1, 5, 3, 0, 0}, {3, 3, 0, 3, 0, 3}, {3, 3, 3, 0, 0, 3}, {3, 3, 3, 3, 0, 0}, {3, 3, 3, 3, 0, 3}, {5, 1, 3, 0, 0, 3}}, {{0, 3, 0, 3, 3, 3}, {0, 5, 0, 1, 3, 3}, {2, 3, 0, 1, 3, 3}, {3, 0, 0, 3, 3, 3}, {3, 2, 0, 1, 3, 3}, {3, 3, 0, 0, 3, 3}, {3, 3, 0, 1, 0, 5}, {3, 3, 0, 1, 2, 3}, {3, 3, 0, 1, 3, 2}, {3, 3, 0, 1, 5, 0}, {3, 3, 0, 3, 0, 3}, {3, 3, 0, 3, 3, 0}, {3, 3, 0, 3, 3, 3}, {5, 0, 0, 1, 3, 3}}, {{0, 3, 1, 0, 5, 3}, {0, 3, 3, 0, 3, 3}, {2, 3, 1, 0, 3, 3}, {3, 0, 1, 0, 3, 5}, {3, 0, 3, 0, 3, 3}, {3, 2, 1, 0, 3, 3}, {3, 3, 0, 0, 3, 3}, {3, 3, 1, 0, 2, 3}, {3, 3, 1, 0, 3, 2}, {3, 3, 3, 0, 0, 3}, {3, 3, 3, 0, 3, 0}, {3, 3, 3, 0, 3, 3}, {3, 5, 1, 0, 3, 0}, {5, 3, 1, 0, 0, 3}}, {{0, 0, 3, 3, 3, 3}, {0, 0, 5, 3, 1, 3}, {2, 0, 3, 3, 1, 3}, {3, 0, 0, 3, 3, 3}, {3, 0, 2, 3, 1, 3}, {3, 0, 3, 0, 1, 5}, {3, 0, 3, 0, 3, 3}, {3, 0, 3, 2, 1, 3}, {3, 0, 3, 3, 0, 3}, {3, 0, 3, 3, 1, 2}, {3, 0, 3, 3, 3, 0}, {3, 0, 3, 3, 3, 3}, {3, 0, 3, 5, 1, 0}, {5, 0, 0, 3, 1, 3}}, {{0, 0, 3, 3, 3, 3}, {0, 0, 5, 3, 3, 1}, {0, 2, 3, 3, 3, 1}, {0, 3, 0, 3, 3, 3}, {0, 3, 2, 3, 3, 1}, {0, 3, 3, 0, 3, 3}, {0, 3, 3, 0, 5, 1}, {0, 3, 3, 2, 3, 1}, {0, 3, 3, 3, 0, 3}, {0, 3, 3, 3, 2, 1}, {0, 3, 3, 3, 3, 0}, {0, 3, 3, 3, 3, 3}, {0, 3, 3, 5, 0, 1}, {0, 5, 0, 3, 3, 1}}, {{0, 0, 3, 3, 0, 0}, {0, 0, 3, 3, 0, 3}, {3, 0, 0, 0, 0, 3}, {3, 0, 0, 3, 0, 3}, {3, 0, 3, 0, 0, 3}, {3, 0, 3, 3, 0, 0}}, {{0, 3, 0, 0, 3, 0}, {0, 3, 0, 0, 3, 3}, {3, 0, 0, 0, 0, 3}, {3, 0, 0, 0, 3, 3}, {3, 3, 0, 0, 0, 3}, {3, 3, 0, 0, 3, 0}}, {{0, 0, 3, 3, 0, 0}, {0, 0, 3, 3, 3, 0}, {0, 3, 0, 0, 3, 0}, {0, 3, 0, 3, 3, 0}, {0, 3, 3, 0, 3, 0}, {0, 3, 3, 3, 0, 0}}}\)], "Output"] }, Open ]], Cell["\<\ The Albouy-Chenciner equations have 14 essentially different monomials and \ the Dziobek equations have 6. These will be the initial numbers of \ vertices in the initial Newton polytopes, but some of them may not be extreme \ points on the convex hull. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Length, explist9]\)], "Input"], Cell[BoxData[ \({14, 14, 14, 14, 14, 14, 6, 6, 6}\)], "Output"] }, Open ]], Cell["\<\ In a similar way, we compute the exponent vectors for the auxiliary system of \ 10 equations and 10 unknowns. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(tenvars\ = \ {r12, r13, r14, r23, r24, r34, z1, z2, z3, z4};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(explist10\ = \ Map[GetAllExponents[#, tenvars] &, teneqs]\[IndentingNewLine]\), "\[IndentingNewLine]", \(Map[Length, explist10]\)}], "Input"], Cell[BoxData[ \({{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 2, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {0, 2, 0, 0, 0, 0, 0, 0, 1, 0}, {2, 0, 0, 0, 0, 0, 0, 1, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 0, 2, 0, 0, 0, 0, 1, 0}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {2, 0, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 2, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 2, 0, 0, 1, 0}, {0, 0, 0, 0, 2, 0, 0, 1, 0, 0}, {0, 0, 0, 2, 0, 0, 0, 1, 0, 0}, {0, 0, 2, 0, 0, 0, 1, 0, 0, 0}, {0, 2, 0, 0, 0, 0, 1, 0, 0, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {3, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {3, 0, 0, 0, 0, 0, 1, 1, 0, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 3, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 3, 0, 0, 0, 0, 1, 0, 1, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 3, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 3, 0, 0, 0, 1, 1, 0}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 0, 0, 1, 0, 0, 1}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 3, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 3, 0, 0, 1, 0, 1}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 3, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 3, 0, 0, 1, 1}}}\)], "Output"], Cell[BoxData[ \({4, 6, 6, 6, 3, 3, 3, 3, 3, 3}\)], "Output"] }, Open ]], Cell["\<\ At this point the exponent list explist10 was put into a data file and edited \ to conform with the syntax requirements of the program Mixvol. The resulting \ file, called teneqs.sites was given as input to that program which \ computed the mixed volume of the 10 polytopes. The result was 25380 as \ reported in section 6 of the paper. After this we have no further need for \ the system of 10 equations or its exponent lists. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Partial Minkowski Sums", "Subsection"], Cell["\<\ A key step in the method is to find the Minkowski sum of the 9 Newton \ polytopes of the Albouy-Chenciner-Dziobek system. The naive way to find a \ Minkowski sum is just to take all possible sums of nine vertices, one from \ each of the Newton polytopes. In practice, we had to go through cycles of \ taking Minkowski sums of a few of the 9 Newton polytopes, finding a more \ efficient representation of the convex hull using Porta and then adding in \ more of the Newton polytopes. In this way we could succeed in finding \ separate Minkowski sums for the six Albouy-Chenciner equations and for the \ three Dziobek equations. To add these two together required some tricks \ which will be handled in the next subsection. \ \>", "Text"], Cell["\<\ We begin with basic functios to add a single vertex to a list of vertices and \ to add two lists of vertices together. The second function is a primitive \ Minkowski sum for two polytopes but the vertex list will be unnecessarily \ long. One needs a program like Porta to find the true extreme points of the \ convex hull. \ \>", "Text"], Cell[BoxData[{ \(AddToAll[vect_, vlist_]\ := Map[\((\ vect + #)\) &, vlist]\), "\[IndentingNewLine]", \(MinkSum[vlist_, wlist_]\ := \ \(Map[AddToAll[#, wlist] &, vlist] // Flatten[#, 1] &\) // Union\)}], "Input"], Cell["\<\ Here is the primitive Minkowski sum for the three Dziobek equations. We get a \ list of 132 vertices. \ \>", "Text"], Cell[BoxData[{ \(dzmink\ = \ MinkSum[MinkSum[explist9[\([7]\)], explist9[\([8]\)]], explist9[\([9]\)]]\), "\[IndentingNewLine]", \(Length[dzmink]\)}], "Input"], Cell[TextData[{ "We put this list in a file named \"dzmink.poi\" and edited it to conform \ with the syntax of the program Porta 1.3.2. Running the command ", StyleBox["traf -l dzmink.poi ", FontWeight->"Bold"], "produces a file called \"dzmink.poi.ieq\" containing a minimal list of \ inequalities in six variables x1, ... , x6 defining the convex hull . \ Running the command ", StyleBox["traf -l dzmink.poi.ieq ", FontWeight->"Bold"], StyleBox["produces yet another file \"dzmink.poi.ieq.poi which contains the \ true vertices of the Minkowski sum polytope. To avoid having to deal with \ these files here, we will just copy the results, showing the commands in \ comments", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[{ \( (*\ Write\ the\ raw\ vertices\ to\ a\ file\ *) \[IndentingNewLine] (*\ Put[dzmink, "\"]\ *) \ \[IndentingNewLine]\[IndentingNewLine] (*\ Read\ in\ the\ results\ from\ porta, \ after\ editing\ the\ output\ files\ to\ Mathematica\ syntax\ *) \ \[IndentingNewLine] (*\ dzconv\ = \ ReadList["\", {Number, Number, Number, Number, Number, Number}]*) (*\ dzineq\ = \ ReadList["\", Expression]*) \[IndentingNewLine]\[IndentingNewLine]\(dzconv\ = \ \ {{3, 6, 0, 0, 6, 3}, {0, 3, 6, 6, 6, 0}, {3, 6, 0, 0, 6, 6}, {3, 6, 0, 6, 6, 6}, {6, 3, 0, 0, 6, 6}, {6, 3, 0, 6, 6, 6}, {0, 3, 6, 6, 3, 0}, {0, 6, 3, 3, 6, 0}, {0, 3, 6, 6, 6, 6}, {0, 6, 3, 6, 6, 0}, {0, 6, 3, 6, 6, 6}, {0, 6, 6, 3, 6, 0}, {0, 6, 6, 3, 6, 6}, {0, 6, 6, 6, 3, 0}, {6, 3, 6, 0, 6, 6}, {0, 3, 6, 6, 3, 6}, {0, 6, 3, 3, 6, 6}, {0, 6, 6, 6, 3, 6}, {6, 6, 0, 0, 3, 6}, {6, 6, 0, 6, 3, 6}, {6, 6, 6, 0, 3, 6}, {6, 0, 3, 3, 0, 6}, {6, 0, 3, 3, 6, 6}, {6, 0, 3, 6, 0, 6}, {6, 0, 3, 6, 6, 6}, {3, 0, 6, 6, 0, 3}, {3, 0, 6, 6, 6, 3}, {3, 0, 6, 6, 0, 6}, {3, 0, 6, 6, 6, 6}, {6, 0, 6, 3, 0, 6}, {6, 0, 6, 3, 6, 6}, {3, 6, 6, 6, 0, 3}, {3, 6, 6, 6, 0, 6}, {6, 6, 3, 3, 0, 6}, {6, 6, 3, 6, 0, 6}, {6, 6, 6, 3, 0, 6}, {6, 0, 6, 6, 0, 3}, {6, 0, 6, 6, 6, 3}, {6, 6, 0, 0, 6, 3}, {6, 6, 0, 6, 6, 3}, {6, 6, 6, 6, 0, 3}, {6, 3, 6, 6, 6, 0}, {6, 3, 6, 6, 3, 0}, {6, 6, 3, 3, 6, 0}, {3, 6, 6, 0, 6, 6}, {6, 6, 3, 6, 6, 0}, {6, 6, 6, 0, 6, 3}, {6, 6, 6, 3, 6, 0}, {3, 6, 0, 6, 6, 3}, {3, 6, 6, 0, 6, 3}, {6, 3, 0, 0, 3, 6}, {6, 3, 0, 6, 3, 6}, {6, 3, 6, 0, 3, 6}, {6, 6, 6, 6, 3, 0}};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(dzineq\ = \ {x1 + x2 + x5 + x6 \[LessEqual] 21, \(-x1\) - x2 - x3 \[LessEqual] \(-9\), \(-x1\) - x2 - x4 \[LessEqual] \(-9\), x3 \[LessEqual] 6, \(-x1\) - x4 - x5 \[LessEqual] \(-9\), x4 \[LessEqual] 6, \(-x1\) - x3 - x5 \[LessEqual] \(-9\), x6 \[LessEqual] 6, x5 \[LessEqual] 6, \(-x6\) \[LessEqual] 0, \(-x2\) - x3 - x6 \[LessEqual] \(-9\), \(-x2\) - x4 - x6 \[LessEqual] \(-9\), \(-x3\) - x5 - x6 \[LessEqual] \(-9\), \(-x4\) - x5 - x6 \[LessEqual] \(-9\), x2 + x3 + x4 + x5 \[LessEqual] 21, \(-x1\) \[LessEqual] 0, x2 \[LessEqual] 6, \(-x2\) \[LessEqual] 0, \(-x5\) \[LessEqual] 0, x1 + x3 + x4 + x6 \[LessEqual] 21, x1 \[LessEqual] 6, \(-x3\) \[LessEqual] 0, \(-x4\) \[LessEqual] 0, x1 + x2 + x3 + x4 + x5 + x6 \[LessEqual] 27};\)\)}], "Input"], Cell["\<\ This is the description of the polytope P2 in section 4.1 of the paper. It \ has 54 vertices and 24 facets. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Length[dzconv]\), "\[IndentingNewLine]", \(Length[dzineq]\)}], "Input"], Cell[BoxData[ \(54\)], "Output"], Cell[BoxData[ \(24\)], "Output"] }, Open ]], Cell["\<\ A similar approach was used for the six Albouy-Chenciner equations. This \ time it is not possible to add all six at once. Instead we had to add three \ of the polytopes, reduce the number of hull vertices with Porta, add in the \ fourth, reduces the hull, etc. Here are the final results. To save space, \ this cell has been kept closed. Select it and open it to see the results. \ In any case, the cell should be selected and executed at this time before \ continuing. \ \>", "Text"], Cell[BoxData[{ \(\(acconv = {{0, 13, 13, 17, 17, 15}, {0, 13, 13, 19, 14, 13}, {0, 10, 15, 17, 17, 13}, {0, 10, 13, 17, 17, 15}, {0, 13, 17, 17, 13, 15}, {0, 13, 17, 19, 10, 13}, {0, 10, 19, 17, 13, 13}, {0, 10, 17, 17, 13, 15}, {0, 13, 17, 17, 10, 15}, {0, 13, 10, 17, 17, 15}, {0, 13, 13, 14, 19, 13}, {0, 13, 13, 17, 17, 12}, {0, 15, 10, 17, 17, 13}, {0, 17, 17, 13, 13, 15}, {0, 17, 17, 15, 10, 13}, {0, 14, 19, 13, 13, 13}, {0, 17, 17, 13, 10, 15}, {0, 17, 13, 13, 17, 15}, {0, 17, 10, 13, 17, 15}, {0, 17, 13, 10, 19, 13}, {0, 19, 10, 13, 17, 13}, {0, 17, 17, 10, 13, 15}, {0, 17, 13, 10, 17, 15}, {0, 17, 17, 10, 15, 13}, {0, 19, 14, 13, 13, 13}, {0, 17, 17, 13, 13, 12}, {0, 17, 13, 13, 17, 12}, {0, 13, 17, 17, 13, 12}, {1, 10, 13, 19, 17, 15}, {1, 10, 13, 21, 14, 13}, {1, 7, 15, 19, 17, 13}, {1, 7, 13, 19, 17, 15}, {1, 10, 17, 19, 13, 15}, {1, 10, 17, 21, 10, 13}, {1, 7, 19, 19, 13, 13}, {1, 7, 17, 19, 13, 15}, {1, 10, 17, 19, 10, 15}, {1, 10, 10, 19, 17, 15}, {1, 13, 10, 17, 19, 15}, {1, 10, 12, 17, 19, 13}, {1, 10, 10, 17, 19, 15}, {1, 13, 10, 14, 21, 13}, {1, 10, 13, 16, 19, 13}, {1, 13, 10, 17, 19, 12}, {1, 13, 7, 17, 19, 15}, {1, 10, 13, 19, 17, 12}, {1, 12, 10, 19, 17, 13}, {1, 15, 7, 17, 19, 13}, {1, 13, 19, 17, 10, 15}, {1, 13, 19, 19, 7, 13}, {1, 10, 21, 17, 10, 13}, {1, 10, 19, 17, 10, 15}, {1, 13, 19, 17, 7, 15}, {1, 10, 17, 19, 13, 12}, {1, 17, 10, 10, 21, 13}, {1, 17, 10, 13, 19, 15}, {1, 17, 7, 13, 19, 15}, {1, 17, 10, 10, 19, 15}, {1, 13, 10, 19, 16, 13}, {3, 13, 13, 15, 19, 12}, {3, 10, 15, 15, 19, 10}, {3, 13, 13, 12, 21, 10}, {3, 13, 13, 15, 19, 9}, {6, 13, 15, 13, 19, 6}, {4, 10, 13, 17, 19, 12}, {4, 7, 15, 17, 19, 10}, {4, 13, 10, 15, 21, 12}, {4, 10, 12, 15, 21, 10}, {4, 13, 10, 12, 23, 10}, {4, 13, 10, 15, 21, 9}, {4, 10, 13, 17, 19, 9}, {1, 17, 19, 13, 10, 15}, {1, 14, 21, 13, 10, 13}, {1, 17, 19, 13, 7, 15}, {1, 17, 19, 10, 10, 15}, {1, 17, 19, 15, 7, 13}, {1, 17, 19, 13, 10, 12}, {1, 13, 19, 17, 10, 12}, {1, 17, 19, 10, 12, 13}, {1, 19, 17, 10, 13, 15}, {1, 16, 19, 10, 13, 13}, {1, 19, 17, 7, 13, 15}, {1, 19, 17, 7, 15, 13}, {1, 19, 7, 13, 19, 13}, {1, 17, 10, 13, 19, 12}, {3, 13, 13, 19, 15, 12}, {3, 13, 13, 21, 12, 10}, {3, 13, 13, 19, 15, 9}, {3, 15, 10, 19, 15, 10}, {6, 15, 13, 19, 13, 6}, {4, 10, 13, 21, 15, 12}, {4, 10, 13, 23, 12, 10}, {4, 13, 10, 19, 17, 9}, {4, 13, 10, 19, 17, 12}, {4, 10, 13, 21, 15, 9}, {4, 12, 10, 21, 15, 10}, {4, 15, 7, 19, 17, 10}, {3, 15, 19, 13, 13, 12}, {3, 12, 21, 13, 13, 10}, {3, 15, 19, 10, 15, 10}, {3, 15, 19, 13, 13, 9}, {6, 13, 19, 13, 15, 6}, {4, 15, 21, 13, 10, 12}, {4, 12, 23, 13, 10, 10}, {4, 15, 21, 13, 10, 9}, {4, 15, 21, 10, 12, 10}, {4, 17, 19, 10, 13, 12}, {4, 17, 19, 7, 15, 10}, {1, 19, 13, 7, 17, 15}, {1, 21, 10, 10, 17, 13}, {1, 19, 13, 10, 17, 15}, {1, 19, 10, 10, 17, 15}, {1, 19, 13, 7, 19, 13}, {1, 19, 17, 12, 10, 13}, {1, 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15, 7, 10}, {21, 10, 7, 15, 4, 15}, {21, 10, 7, 13, 4, 17}, {23, 7, 10, 12, 7, 13}, {21, 7, 4, 10, 13, 17}, {21, 7, 10, 7, 15, 15}, {21, 7, 7, 7, 15, 15}, {21, 12, 7, 7, 15, 10}, {21, 12, 10, 7, 15, 10}, {21, 10, 12, 7, 15, 10}, {21, 7, 12, 7, 15, 10}, {21, 7, 15, 7, 10, 15}, {21, 4, 15, 7, 10, 15}, {21, 7, 15, 7, 7, 15}, {21, 10, 13, 7, 4, 17}, {21, 4, 13, 7, 10, 17}, {21, 7, 10, 4, 15, 15}, {21, 7, 10, 4, 13, 17}, {23, 7, 10, 7, 12, 13}, {23, 10, 7, 7, 12, 13}, {23, 10, 7, 12, 7, 13}, {21, 4, 15, 7, 12, 13}, {21, 7, 15, 12, 7, 10}, {21, 7, 15, 12, 10, 10}, {21, 7, 15, 10, 12, 10}, {21, 7, 15, 7, 12, 10}, {21, 7, 13, 10, 12, 9}, {21, 7, 13, 12, 10, 9}, {21, 7, 12, 4, 15, 13}, {21, 10, 12, 7, 13, 9}, {21, 12, 10, 7, 13, 9}, {21, 10, 12, 13, 7, 9}, {21, 12, 10, 13, 7, 9}, {21, 12, 7, 15, 4, 13}, {23, 7, 12, 10, 7, 13}, {23, 7, 12, 7, 10, 13}, {21, 13, 10, 4, 7, 17}, {21, 15, 7, 10, 7, 15}, {21, 15, 4, 10, 7, 15}, {21, 15, 7, 7, 7, 15}, {21, 13, 4, 10, 7, 17}, {21, 13, 7, 12, 10, 9}, {21, 15, 7, 7, 12, 10}, {21, 15, 7, 10, 12, 10}, {21, 13, 7, 10, 12, 9}, {21, 15, 7, 12, 10, 10}, {21, 15, 7, 12, 7, 10}, {23, 12, 7, 7, 10, 13}, {23, 12, 7, 10, 7, 13}, {21, 15, 4, 12, 7, 13}, {23, 12, 7, 10, 10, 13}};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(acineq\ = \ {\(-x1\) \[LessEqual] 0, x3\/45 + x5\/45 + x6\/45 \[LessEqual] 1, \(-\(x1\/72\)\) - x2\/72 - x3\/72 - x4\/72 - x5\/72 - x6\/72 \[LessEqual] \(-1\), \(-\(\(2\ x1\)\/35\)\) + \(2\ \ x3\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(x1\/16\)\) + x4\/32 + x6\/32 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(3\ x4\)\/85 + \(2\ x5\)\/85 \ \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(4\ x2\)\/385 + \(6\ x3\)\/385 + \ \(9\ x4\)\/385 + \(6\ x5\)\/385 \[LessEqual] 1, \(-\(\(2\ x1\)\/49\)\) + x3\/49 + x4\/49 + x6\/49 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(2\ x4\)\/85 + \(3\ x5\)\/85 \ \[LessEqual] 1, \(-\(x1\/16\)\) + x5\/32 + x6\/32 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, x3\/61 + \(3\ x5\)\/122 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(x1\/17\)\) + x4\/34 + x5\/34 \[LessEqual] 1, \(-\(x1\/16\)\) + x3\/32 + x6\/32 \[LessEqual] 1, \(3\ x3\)\/122 + x5\/61 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(6\ x2\)\/385 + \(9\ x3\)\/385 + \ \(6\ x4\)\/385 + \(4\ x5\)\/385 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + \(2\ x2\)\/175 + x3\/35 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, x2\/77 + \(3\ x3\)\/154 + \(3\ x4\)\/154 + x5\/77 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + \(2\ x2\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, x2\/45 + x4\/45 + x6\/45 \[LessEqual] 1, x2\/61 + \(3\ x4\)\/122 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(6\ x2\)\/385 + \(4\ x3\)\/385 + \ \(6\ x4\)\/385 + \(9\ x5\)\/385 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(2\ x2\)\/85 + \(3\ x3\)\/85 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + \(2\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x1\)\/49\)\) + x2\/49 + x5\/49 + x6\/49 \[LessEqual] 1, \(-\(x1\/16\)\) + x2\/32 + x6\/32 \[LessEqual] 1, \(3\ x2\)\/122 + x4\/61 + \(3\ x6\)\/122 \[LessEqual] 1, \(-\(\(2\ x1\)\/35\)\) + x2\/35 + \(2\ x3\)\/175 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(-\(\(6\ x1\)\/385\)\) + \(9\ x2\)\/385 + \(6\ x3\)\/385 + \ \(4\ x4\)\/385 + \(6\ x5\)\/385 \[LessEqual] 1, \(3\ x2\)\/154 + x3\/77 + x4\/77 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(6\ x1\)\/85\)\) + \(3\ x2\)\/85 + \(2\ x3\)\/85 \ \[LessEqual] 1, \(-\(x1\/17\)\) + x2\/34 + x3\/34 \[LessEqual] 1, \(-\(\(4\ x1\)\/175\)\) + x2\/35 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(-\(\(2\ x1\)\/45\)\) + x6\/15 \[LessEqual] 1, \(-\(x1\/31\)\) + x4\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(x1\/47\)\) + x4\/94 + x5\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(x1\/47\)\) + x3\/94 + x4\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(x1\/31\)\) + x5\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(x1\/225\)\) + x2\/75 + x3\/50 + x4\/75 + x5\/50 \[LessEqual] 1, \(2\ x2\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(4\ x2\)\/419 + \(6\ x3\)\/419 + \ \(7\ x4\)\/419 + \(10\ x5\)\/419 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(32\ x2\)\/3335 + \(48\ \ x3\)\/3335 + \(54\ x4\)\/3335 + \(81\ x5\)\/3335 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(8\ x2\)\/945 + \(2\ x3\)\/135 + \ \(2\ x4\)\/135 + \(23\ x5\)\/945 + \(2\ x6\)\/945 \[LessEqual] 1, \(-\(x1\/31\)\) + x3\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(18\ x2\)\/1207 + \(27\ x3\)\/1207 \ + \(18\ x4\)\/1207 + \(16\ x5\)\/1207 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(54\ x2\)\/3335 + \(81\ \ x3\)\/3335 + \(32\ x4\)\/3335 + \(48\ x5\)\/3335 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(2\ x2\)\/135 + \(23\ x3\)\/945 + \ \(8\ x4\)\/945 + \(2\ x5\)\/135 + \(2\ x6\)\/945 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(18\ x2\)\/1207 + \(16\ x3\)\/1207 \ + \(18\ x4\)\/1207 + \(27\ x5\)\/1207 \[LessEqual] 1, \(3\ x2\)\/167 + \(2\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/225\)\) + x2\/50 + x3\/75 + x4\/50 + x5\/75 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(48\ x2\)\/3335 + \(32\ \ x3\)\/3335 + \(81\ x4\)\/3335 + \(54\ x5\)\/3335 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(16\ x2\)\/1207 + \(18\ x3\)\/1207 \ + \(27\ x4\)\/1207 + \(18\ x5\)\/1207 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(6\ x2\)\/419 + \(4\ x3\)\/419 + \ \(10\ x4\)\/419 + \(7\ x5\)\/419 \[LessEqual] 1, x2\/60 + x3\/60 + x4\/60 + x5\/60 \[LessEqual] 1, x2\/77 + x3\/77 + \(3\ x4\)\/154 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(2\ x2\)\/135 + \(8\ x3\)\/945 + \ \(23\ x4\)\/945 + \(2\ x5\)\/135 + \(2\ x6\)\/945 \[LessEqual] 1, \(3\ x2\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(2\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/47\)\) + x2\/94 + x5\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(3\ x2\)\/167 + \(3\ x3\)\/167 + \(2\ x4\)\/167 + \(3\ \ x5\)\/167 \[LessEqual] 1, \(-\(x1\/47\)\) + x2\/94 + x3\/94 + \(2\ x6\)\/47 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(7\ x2\)\/419 + \(10\ x3\)\/419 + \ \(4\ x4\)\/419 + \(6\ x5\)\/419 \[LessEqual] 1, \(-\(x1\/31\)\) + x2\/62 + \(3\ x6\)\/62 \[LessEqual] 1, \(-\(\(6\ x1\)\/1207\)\) + \(27\ x2\)\/1207 + \(18\ x3\)\/1207 \ + \(16\ x4\)\/1207 + \(18\ x5\)\/1207 \[LessEqual] 1, \(-\(\(2\ x1\)\/419\)\) + \(10\ x2\)\/419 + \(7\ x3\)\/419 + \ \(6\ x4\)\/419 + \(4\ x5\)\/419 \[LessEqual] 1, \(-\(\(18\ x1\)\/3335\)\) + \(81\ x2\)\/3335 + \(54\ \ x3\)\/3335 + \(48\ x4\)\/3335 + \(32\ x5\)\/3335 \[LessEqual] 1, \(3\ x2\)\/154 + \(3\ x3\)\/154 + x4\/77 + x5\/77 \[LessEqual] 1, \(-\(\(4\ x1\)\/945\)\) + \(23\ x2\)\/945 + \(2\ x3\)\/135 + \ \(2\ x4\)\/135 + \(8\ x5\)\/945 + \(2\ x6\)\/945 \[LessEqual] 1, \(2\ x3\)\/185 + x4\/37 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x4\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x4\/36 + x5\/36 \[LessEqual] 1, x4\/51 + x5\/51 + x6\/51 \[LessEqual] 1, \(5\ x4\)\/159 + \(2\ x5\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, x3\/51 + x4\/51 + x6\/51 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(9\ x4\)\/271 + \(6\ x5\)\/271 \ \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(4\ x2\)\/389 + \(6\ x3\)\/389 + \ \(9\ x4\)\/389 + \(6\ x5\)\/389 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x5\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x4\)\/159 + \(5\ x5\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(6\ x4\)\/271 + \(9\ x5\)\/271 \ \[LessEqual] 1, \(4\ x2\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(9\ \ x5\)\/391 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x3\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(2\ x2\)\/185 + x3\/37 + \(2\ x4\)\/185 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(6\ x2\)\/389 + \(9\ x3\)\/389 + \ \(6\ x4\)\/389 + \(4\ x5\)\/389 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(6\ x2\)\/271 + \(9\ x3\)\/271 \ \[LessEqual] 1, \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x2\)\/159 + \(5\ x3\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(2\ x2\)\/185 + \(2\ x4\)\/185 + x5\/37 + \(2\ x6\)\/185 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(6\ x2\)\/389 + \(4\ x3\)\/389 + \ \(6\ x4\)\/389 + \(9\ x5\)\/389 \[LessEqual] 1, \(6\ x2\)\/391 + \(4\ x3\)\/391 + \(9\ x4\)\/391 + \(6\ \ x5\)\/391 \[LessEqual] 1, \(6\ x2\)\/391 + \(9\ x3\)\/391 + \(4\ x4\)\/391 + \(6\ \ x5\)\/391 \[LessEqual] 1, x2\/51 + x5\/51 + x6\/51 \[LessEqual] 1, x2\/36 + x3\/36 \[LessEqual] 1, x2\/51 + x3\/51 + x6\/51 \[LessEqual] 1, \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(-\(x1\/50\)\) + \(3\ x2\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, x2\/37 + \(2\ x3\)\/185 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(5\ x2\)\/159 + \(2\ x3\)\/159 + \(2\ x6\)\/159 \[LessEqual] 1, \(-\(\(2\ x1\)\/389\)\) + \(9\ x2\)\/389 + \(6\ x3\)\/389 + \ \(4\ x4\)\/389 + \(6\ x5\)\/389 \[LessEqual] 1, \(-\(\(2\ x1\)\/271\)\) + \(9\ x2\)\/271 + \(6\ x3\)\/271 \ \[LessEqual] 1, \(9\ x2\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(4\ \ x5\)\/391 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x4\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x5\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x3\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(2\ x2\)\/139 + \(3\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x4\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(2\ x2\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(3\ \ x5\)\/139 \[LessEqual] 1, \(2\ x2\)\/139 + \(2\ x3\)\/139 + \(3\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \ \(2\ x4\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(-\(\(2\ x1\)\/79\)\) + x2\/79 + \(4\ x6\)\/79 \[LessEqual] 1, \(-\(\(4\ x1\)\/265\)\) + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \ \(2\ x5\)\/265 + \(11\ x6\)\/265 \[LessEqual] 1, \(3\ x2\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x5\)\/139 \[LessEqual] 1, x4\/36 + x6\/36 \[LessEqual] 1, \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(-\(\(4\ x2\)\/265\)\) + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \ \(11\ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(-\(x2\/31\)\) + x4\/62 + \(3\ x5\)\/62 \[LessEqual] 1, \(-\(x2\/47\)\) + x4\/94 + \(2\ x5\)\/47 + x6\/94 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + x4\/79 + \(4\ x5\)\/79 \[LessEqual] 1, x4\/31 + \(2\ x5\)\/93 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x4\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(3\ x3\)\/122 + \(3\ x5\)\/122 + x6\/61 \[LessEqual] 1, x3\/51 + x4\/51 + x5\/51 \[LessEqual] 1, \(-\(x2\/47\)\) + x3\/94 + x4\/94 + \(2\ x5\)\/47 \[LessEqual] 1, x5\/36 + x6\/36 \[LessEqual] 1, \(-\(\(4\ x2\)\/245\)\) + \(2\ x4\)\/245 + \(11\ x5\)\/245 + \ \(2\ x6\)\/245 \[LessEqual] 1, \(2\ x3\)\/109 + \(3\ x5\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(-\(\(4\ x2\)\/245\)\) + \(2\ x3\)\/245 + \(2\ x4\)\/245 + \ \(11\ x5\)\/245 \[LessEqual] 1, \(4\ x2\)\/655 + \(12\ x3\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(4\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, \(4\ x2\)\/307 + \(9\ x4\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x4\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x3\)\/165 + x4\/33 + \(2\ x6\)\/165 \[LessEqual] 1, \(4\ x2\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, \(2\ x3\)\/165 + x4\/33 + \(2\ x5\)\/165 \[LessEqual] 1, x3\/36 + x6\/36 \[LessEqual] 1, \(3\ x3\)\/109 + \(2\ x5\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, x3\/38 + x4\/38 \[LessEqual] 1, \(2\ x4\)\/93 + x5\/31 \[LessEqual] 1, \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(-\(\(4\ x3\)\/245\)\) + \(11\ x4\)\/245 + \(2\ x5\)\/245 + \ \(2\ x6\)\/245 \[LessEqual] 1, \(-\(\(2\ x3\)\/79\)\) + \(4\ x4\)\/79 + x5\/79 \[LessEqual] 1, \(-\(x3\/47\)\) + \(2\ x4\)\/47 + x5\/94 + x6\/94 \[LessEqual] 1, \(4\ x3\)\/307 + \(9\ x5\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(2\ x4\)\/179 + \(9\ x5\)\/179 \ \[LessEqual] 1, \(2\ x2\)\/109 + \(3\ x4\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(-\(\(4\ x3\)\/179\)\) + \(9\ x4\)\/179 + \(2\ x5\)\/179 \ \[LessEqual] 1, \(6\ x3\)\/307 + \(9\ x5\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(4\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\/629 + \(15\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/131 + \(6\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ x4\)\/629 + \(6\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, x4\/23 \[LessEqual] 1, \(6\ x2\)\/307 + \(9\ x4\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(2\ x2\)\/245 - \(4\ x3\)\/245 + \(11\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(9\ x3\)\/307 + \(4\ x5\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x3\/33 + \(2\ x4\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(6\ x4\)\/655 + \(2\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, x3\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x2\)\/93 + x3\/31 \[LessEqual] 1, \(6\ x2\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(4\ \ x5\)\/397 \[LessEqual] 1, \(9\ x3\)\/307 + \(6\ x5\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x2\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, x3\/23 \[LessEqual] 1, \(2\ x2\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(2\ x2\)\/179 + \(9\ x3\)\/179 - \(4\ x4\)\/179 \[LessEqual] 1, \(2\ x2\)\/165 + x3\/33 + \(2\ x4\)\/165 \[LessEqual] 1, \(6\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\/629 + \(10\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(-\(x3\/50\)\) + \(3\ x4\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(-\(x3\/31\)\) + \(3\ x4\)\/62 + x5\/62 \[LessEqual] 1, \(3\ x2\)\/122 + \(3\ x4\)\/122 + x6\/61 \[LessEqual] 1, \(6\ x2\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(9\ \ x5\)\/397 \[LessEqual] 1, x5\/23 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x4\)\/165 + x5\/33 \[LessEqual] 1, \(6\ x2\)\/655 + \(2\ x3\)\/131 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(12\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(4\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, x2\/51 + x3\/51 + x4\/51 \[LessEqual] 1, \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ x4\)\/655 + \(12\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x2\/51 + x4\/51 + x5\/51 \[LessEqual] 1, x5\/31 + \(2\ x6\)\/93 \[LessEqual] 1, \(2\ x2\)\/165 + x5\/33 + \(2\ x6\)\/165 \[LessEqual] 1, \(6\ x2\)\/565 + \(4\ x3\)\/565 + \(6\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, x2\/79 + \(4\ x3\)\/79 - \(2\ x4\)\/79 \[LessEqual] 1, x2\/94 - x3\/47 + \(2\ x4\)\/47 + x5\/94 \[LessEqual] 1, x2\/36 + x6\/36 \[LessEqual] 1, x2\/38 + x5\/38 \[LessEqual] 1, x2\/94 + \(2\ x3\)\/47 - x4\/47 + x6\/94 \[LessEqual] 1, x2\/51 + x3\/51 + x5\/51 \[LessEqual] 1, x2\/94 + \(2\ x3\)\/47 - x4\/47 + x5\/94 \[LessEqual] 1, \(11\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ x4\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(3\ x2\)\/62 + x3\/62 - x5\/31 \[LessEqual] 1, \(2\ x2\)\/47 + x3\/94 - x5\/47 + x6\/94 \[LessEqual] 1, \(3\ x2\)\/100 + \(3\ x3\)\/100 - x5\/50 \[LessEqual] 1, \(4\ x2\)\/79 + x3\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(12\ x4\)\/655 + \(4\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(15\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ x4\)\/629 + \(4\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x2\)\/47 + x3\/94 + x4\/94 - x5\/47 \[LessEqual] 1, \(3\ x2\)\/109 + \(2\ x4\)\/109 + \(2\ x6\)\/109 \[LessEqual] 1, \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ x5\)\/179 + \(5\ \ x6\)\/179 \[LessEqual] 1, \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(4\ x4\)\/565 + \(6\ \ x5\)\/565 + \(3\ x6\)\/113 \[LessEqual] 1, \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(2\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x2\/62 + \(3\ x3\)\/62 - x4\/31 \[LessEqual] 1, \(11\ x2\)\/245 + \(2\ x3\)\/245 - \(4\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(11\ x2\)\/245 + \(2\ x3\)\/245 + \(2\ x4\)\/245 - \(4\ \ x5\)\/245 \[LessEqual] 1, \(9\ x2\)\/307 + \(4\ x4\)\/307 + \(6\ x6\)\/307 \[LessEqual] 1, x2\/33 + \(2\ x5\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(9\ x2\)\/307 + \(6\ x4\)\/307 + \(4\ x6\)\/307 \[LessEqual] 1, x2\/31 + \(2\ x3\)\/93 \[LessEqual] 1, \(3\ x2\)\/100 + \(3\ x3\)\/100 - x4\/50 \[LessEqual] 1, \(9\ x2\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x2\/33 + \(2\ x3\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, \(9\ x2\)\/179 + \(2\ x3\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, x2\/31 + \(2\ x6\)\/93 \[LessEqual] 1, x2\/23 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x4\)\/245 + \(2\ x5\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x3\)\/245 + \(2\ x4\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(2\ x3\)\/109 + \(2\ x5\)\/109 + \(3\ x6\)\/109 \[LessEqual] 1, \(2\ x2\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \(2\ \ x5\)\/195 + x6\/39 \[LessEqual] 1, \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(6\ x4\)\/545 + \(4\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, x2\/120 + x3\/48 + x4\/120 + x5\/48 + x6\/120 \[LessEqual] 1, x2\/77 + \(3\ x3\)\/154 + x4\/77 + \(3\ x5\)\/154 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x2\)\/245 + \(2\ x5\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(-\(\(4\ x1\)\/245\)\) + \(2\ x2\)\/245 + \(2\ x3\)\/245 + \ \(11\ x6\)\/245 \[LessEqual] 1, \(2\ x2\)\/109 + \(2\ x4\)\/109 + \(3\ x6\)\/109 \[LessEqual] 1, x2\/48 + x3\/120 + x4\/48 + x5\/120 + x6\/120 \[LessEqual] 1, x2\/75 + x3\/75 + x4\/50 + x5\/50 - x6\/225 \[LessEqual] 1, \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(4\ x4\)\/545 + \(6\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(3\ x2\)\/154 + x3\/77 + \(3\ x4\)\/154 + x5\/77 \[LessEqual] 1, x2\/50 + x3\/50 + x4\/75 + x5\/75 - x6\/225 \[LessEqual] 1, \(2\ x1\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, x1\/61 + \(3\ x4\)\/122 + \(3\ x5\)\/122 \[LessEqual] 1, \(-\(x2\/17\)\) + x4\/34 + x6\/34 \[LessEqual] 1, \(-\(\(4\ x2\)\/175\)\) + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \ \(2\ x5\)\/175 + x6\/35 \[LessEqual] 1, \(8\ x1\)\/945 - \(4\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(2\ x5\)\/945 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/419 - \(2\ x2\)\/419 + \(6\ x3\)\/419 + \(7\ \ x4\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(4\ x1\)\/655 + \(12\ x3\)\/655 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(-\(\(2\ x2\)\/35\)\) + \(2\ x3\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(4\ x1\)\/307 + \(9\ x4\)\/307 + \(6\ x5\)\/307 \[LessEqual] 1, \(-\(\(2\ x2\)\/271\)\) + \(9\ x4\)\/271 + \(6\ x6\)\/271 \ \[LessEqual] 1, \(-\(x2\/16\)\) + x4\/32 + x5\/32 \[LessEqual] 1, \(4\ x1\)\/385 - \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(9\ \ x4\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(4\ x1\)\/389 - \(2\ x2\)\/389 + \(6\ x3\)\/389 + \(9\ \ x4\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(-\(\(6\ x2\)\/85\)\) + \(3\ x4\)\/85 + \(2\ x6\)\/85 \ \[LessEqual] 1, x1\/77 + \(3\ x3\)\/154 + \(3\ x4\)\/154 + x6\/77 \[LessEqual] 1, \(-\(\(2\ x2\)\/49\)\) + x3\/49 + x4\/49 + x5\/49 \[LessEqual] 1, \(-\(\(2\ x2\)\/45\)\) + x5\/15 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x4\)\/159 + \(2\ x5\)\/159 + \(5\ x6\)\/159 \[LessEqual] 1, \(4\ x1\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(9\ \ x6\)\/391 \[LessEqual] 1, \(4\ x1\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(4\ x1\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + \(4\ x5\)\/79 + x6\/79 \[LessEqual] 1, \(-\(\(2\ x2\)\/79\)\) + x3\/79 + \(4\ x5\)\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(4\ x3\)\/545 + \(6\ x4\)\/545 + \(3\ \ x5\)\/109 + \(6\ x6\)\/545 \[LessEqual] 1, \(-\(\(2\ x3\)\/79\)\) + \(4\ x4\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ x4\)\ \/777 + \(4\ x5\)\/777 + \(19\ x6\)\/777 \[LessEqual] 1, \(-\(\(4\ x3\)\/179\)\) + \(9\ x4\)\/179 + \(2\ x6\)\/179 \ \[LessEqual] 1, x3\/36 + x5\/36 \[LessEqual] 1, x1\/135 + x2\/135 + x3\/54 + x4\/54 + x5\/135 + x6\/135 \[LessEqual] 1, \(4\ x2\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x3\/31 + \(2\ x5\)\/93 \[LessEqual] 1, x3\/33 + \(2\ x4\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, \(4\ x1\)\/307 + \(6\ x4\)\/307 + \(9\ x5\)\/307 \[LessEqual] 1, x1\/180 + x2\/180 + x3\/72 + x4\/72 + x5\/180 + x6\/45 \[LessEqual] 1, \(4\ x1\)\/1041 + \(4\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x1\/180 + x2\/180 + x3\/72 + x4\/72 + x5\/45 + x6\/180 \[LessEqual] 1, \(4\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ x4\)\ \/777 + \(19\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x3\)\/545 + \(6\ x4\)\/545 + \(3\ \ x5\)\/109 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1041 + \(4\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(-\(\(2\ x3\)\/45\)\) + x4\/15 \[LessEqual] 1, \(4\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x4\)\/109 + \(6\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x2\)\/179 - \(4\ x3\)\/179 + \(9\ x4\)\/179 \[LessEqual] 1, \(2\ x3\)\/93 + x5\/31 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x4\/48 + x5\/48 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/145 + \(4\ x3\)\/1015 + \(5\ x4\)\ \/203 + \(2\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(19\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(6\ x2\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(4\ \ x5\)\/397 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x3\)\/165 + x4\/33 \[LessEqual] 1, \(4\ x1\)\/307 + \(6\ x2\)\/307 + \(9\ x3\)\/307 \[LessEqual] 1, x3\/15 - \(2\ x4\)\/45 \[LessEqual] 1, \(9\ x3\)\/179 - \(4\ x4\)\/179 + \(2\ x6\)\/179 \[LessEqual] 1, \(9\ x3\)\/179 - \(4\ x4\)\/179 + \(2\ x5\)\/179 \[LessEqual] 1, \(4\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x3\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(19\ x3\)\/777 + \(4\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x3\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/145 + \(2\ x6\)\/203 \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(9\ x5\)\/179 + \(2\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x2\)\/179\)\) + \(2\ x3\)\/179 + \(9\ x5\)\/179 \ \[LessEqual] 1, \(4\ x1\)\/1015 + \(4\ x2\)\/1015 + \(2\ x3\)\/145 + \(2\ x4\)\ \/203 + \(5\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/315 + \(2\ x2\)\/315 + \(2\ x3\)\/315 + x4\/63 + x5\/63 + x6\/63 \[LessEqual] 1, \(2\ x2\)\/93 + x4\/31 \[LessEqual] 1, \(4\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x4\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/419 + \(7\ x3\)\/419 + \(6\ x4\)\/419 - \(2\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 - \(4\ x5\)\/945 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x4\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, \(4\ x3\)\/79 - \(2\ x4\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x3\)\/79 - \(2\ x4\)\/79 + x5\/79 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(9\ x3\)\/271 - \(2\ x5\)\/271 + \(6\ x6\)\/271 \[LessEqual] 1, \(4\ x1\)\/389 + \(9\ x3\)\/389 + \(6\ x4\)\/389 - \(2\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(2\ x1\)\/167 + \(3\ x2\)\/167 + \(3\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(-\(x3\/17\)\) + x5\/34 + x6\/34 \[LessEqual] 1, \(2\ x2\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(2\ x2\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x3\)\/271\)\) + \(9\ x5\)\/271 + \(6\ x6\)\/271 \ \[LessEqual] 1, \(-\(x3\/16\)\) + x4\/32 + x5\/32 \[LessEqual] 1, \(-\(\(6\ x3\)\/85\)\) + \(3\ x5\)\/85 + \(2\ x6\)\/85 \ \[LessEqual] 1, \(4\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x3\)\/389 + \(9\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(4\ x1\)\/391 + \(6\ x2\)\/391 + \(6\ x5\)\/391 + \(9\ \ x6\)\/391 \[LessEqual] 1, \(4\ x1\)\/397 + \(6\ x2\)\/397 + \(9\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(4\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ \ x4\)\/777 + \(10\ x5\)\/777 + \(19\ x6\)\/777 \[LessEqual] 1, \(6\ x2\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(9\ \ x5\)\/397 \[LessEqual] 1, \(2\ x2\)\/165 + \(2\ x3\)\/165 + x5\/33 \[LessEqual] 1, \(4\ x1\)\/1041 + \(16\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/61 + \(3\ x2\)\/122 + \(3\ x3\)\/122 \[LessEqual] 1, x1\/120 + x2\/48 + x3\/48 + x4\/120 + x5\/120 \[LessEqual] 1, \(4\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x3\)\/385 + \(9\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(4\ x1\)\/419 + \(6\ x2\)\/419 - \(2\ x3\)\/419 + \(7\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/135 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(2\ x5\)\/135 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/655 + \(12\ x2\)\/655 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/77 + \(3\ x2\)\/154 + \(3\ x5\)\/154 + x6\/77 \[LessEqual] 1, x2\/79 - \(2\ x3\)\/79 + \(4\ x4\)\/79 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/180 + x4\/180 + x5\/72 + x6\/45 \[LessEqual] 1, \(4\ x1\)\/1041 + \(16\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x1\/135 + x2\/54 + x3\/135 + x4\/135 + x5\/54 + x6\/135 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/180 + x4\/45 + x5\/72 + x6\/180 \[LessEqual] 1, x2\/36 + x4\/36 \[LessEqual] 1, \(2\ x2\)\/159 + \(2\ x3\)\/159 + \(5\ x6\)\/159 \[LessEqual] 1, x1\/180 + x2\/72 + x3\/45 + x4\/180 + x5\/72 + x6\/180 \[LessEqual] 1, \(2\ x2\)\/175 + x3\/35 + \(2\ x4\)\/175 - \(2\ x5\)\/35 + \(2\ x6\)\/175 \ \[LessEqual] 1, x3\/34 - x5\/17 + x6\/34 \[LessEqual] 1, \(2\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(4\ x1\)\/385 + \(9\ x3\)\/385 + \(6\ x4\)\/385 - \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(3\ x3\)\/85 - \(6\ x5\)\/85 + \(2\ x6\)\/85 \[LessEqual] 1, x2\/32 + x3\/32 - x5\/16 \[LessEqual] 1, x2\/49 + x3\/49 + x4\/49 - \(2\ x5\)\/49 \[LessEqual] 1, x2\/49 - \(2\ x3\)\/49 + x4\/49 + x5\/49 \[LessEqual] 1, \(8\ x1\)\/945 + \(2\ x2\)\/135 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(2\ x5\)\/135 + \(23\ x6\)\/945 \[LessEqual] 1, \(4\ x1\)\/419 + \(7\ x2\)\/419 - \(2\ x4\)\/419 + \(6\ \ x5\)\/419 + \(10\ x6\)\/419 \[LessEqual] 1, \(4\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(4\ x1\)\/1041 + \(10\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(25\ x6\)\/1041 \[LessEqual] 1, x2\/15 - \(2\ x5\)\/45 \[LessEqual] 1, \(4\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/315 + x2\/63 + x3\/63 + \(2\ x4\)\/315 + \(2\ x5\)\/315 + x6\/63 \[LessEqual] 1, x1\/180 + x2\/45 + x3\/72 + x4\/72 + x5\/180 + x6\/180 \[LessEqual] 1, \(4\ x1\)\/1041 + \(25\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(4\ x1\)\/1015 + \(5\ x2\)\/203 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, x2\/34 - x4\/17 + x6\/34 \[LessEqual] 1, x2\/49 + x3\/49 - \(2\ x4\)\/49 + x5\/49 \[LessEqual] 1, \(4\ x2\)\/79 - \(2\ x5\)\/79 + x6\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(3\ x2\)\/109 + \(6\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/777 + \(19\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ \ x4\)\/777 + \(4\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(4\ x2\)\/79 + x4\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(4\ x1\)\/545 + \(3\ x2\)\/109 + \(6\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(9\ x2\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x5\)\/397 \[LessEqual] 1, x2\/33 + \(2\ x4\)\/165 + \(2\ x5\)\/165 \[LessEqual] 1, x2\/31 + \(2\ x4\)\/93 \[LessEqual] 1, x2\/35 + \(2\ x3\)\/175 - \(2\ x4\)\/35 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(9\ x2\)\/271 - \(2\ x4\)\/271 + \(6\ x6\)\/271 \[LessEqual] 1, \(4\ x1\)\/389 + \(9\ x2\)\/389 - \(2\ x4\)\/389 + \(6\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, x2\/32 + x3\/32 - x4\/16 \[LessEqual] 1, \(4\ x1\)\/307 + \(9\ x2\)\/307 + \(6\ x3\)\/307 \[LessEqual] 1, \(4\ x1\)\/385 + \(9\ x2\)\/385 - \(6\ x4\)\/385 + \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(3\ x2\)\/85 - \(6\ x4\)\/85 + \(2\ x6\)\/85 \[LessEqual] 1, \(4\ x1\)\/397 + \(9\ x2\)\/397 + \(6\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x2\)\/179 - \(4\ x5\)\/179 + \(2\ x6\)\/179 \[LessEqual] 1, \(9\ x2\)\/179 + \(2\ x4\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x4\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/139 + \(3\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x3\)\/265 + \(11\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/185 + x3\/37 + \(2\ x4\)\/185 + \(2\ x5\)\/185 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x4\)\/265 + \(11\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + x5\/39 + \(2\ x6\)\/195 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 + \(11\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x3\)\/565 + \(6\ x4\)\/565 + \(3\ \ x5\)\/113 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x4\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x3\)\/307 + \(6\ x5\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(6\ x3\)\/307 + \(4\ x5\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x4\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x5\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x3\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(6\ x1\)\/391 + \(4\ x3\)\/391 + \(9\ x4\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x3\)\/139 + \(3\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x3\)\/245 + \(11\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x3\)\/245 - \(4\ x4\)\/245 + \(2\ \ x5\)\/245 \[LessEqual] 1, \(6\ x1\)\/391 + \(9\ x3\)\/391 + \(4\ x4\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/159 + \(5\ x3\)\/159 + \(2\ x5\)\/159 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x2\)\/195 + x4\/39 + \(2\ x5\)\/195 + \(2\ x6\)\/195 \[LessEqual] 1, \(6\ x2\)\/307 + \(4\ x4\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(4\ x2\)\/307 + \(6\ x4\)\/307 + \(9\ x6\)\/307 \[LessEqual] 1, \(-\(\(4\ x1\)\/179\)\) + \(2\ x2\)\/179 + \(9\ x6\)\/179 \ \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x4\/37 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(5\ \ x5\)\/179 \[LessEqual] 1, \(4\ x2\)\/419 + \(7\ x3\)\/419 + \(6\ x4\)\/419 + \(10\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ \ x4\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/195 + \(2\ x2\)\/195 + x3\/39 + \(2\ x5\)\/195 + \(2\ x6\)\/195 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(4\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 + \(11\ x3\)\/265 - \(4\ \ x4\)\/265 + \(2\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(48\ x2\)\/3335 + \(81\ x3\)\/3335 + \(32\ x4\)\/3335 + \(54\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/419 + \(10\ x3\)\/419 + \(4\ x4\)\/419 + \(7\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(16\ x2\)\/1207 + \(27\ x3\)\/1207 + \(18\ x4\)\/1207 + \(18\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(4\ x2\)\/389 + \(9\ x3\)\/389 + \(6\ x4\)\/389 + \(6\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(9\ x3\)\/271 + \(6\ x5\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x3\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(6\ x1\)\/391 + \(4\ x2\)\/391 + \(9\ x5\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x2\)\/139 + \(3\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x2\)\/245 + \(11\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(2\ x2\)\/245 - \(4\ x3\)\/245 + \(11\ \ x4\)\/245 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ \ x4\)\/265 + \(2\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(6\ \ x5\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(2\ x1\)\/245 - \(4\ x2\)\/245 + \(2\ x3\)\/245 + \(11\ \ x5\)\/245 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x5\/37 \[LessEqual] 1, \(2\ x1\)\/159 + \(2\ x3\)\/159 + \(5\ x5\)\/159 \[LessEqual] 1, \(32\ x2\)\/3335 + \(54\ x3\)\/3335 + \(48\ x4\)\/3335 + \(81\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(18\ x2\)\/1207 + \(18\ x3\)\/1207 + \(16\ x4\)\/1207 + \(27\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(6\ x3\)\/271 + \(9\ x5\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(6\ x2\)\/389 + \(6\ x3\)\/389 + \(4\ x4\)\/389 + \(9\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(18\ x2\)\/1207 + \(18\ x3\)\/1207 + \(27\ x4\)\/1207 + \(16\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(6\ x2\)\/389 + \(6\ x3\)\/389 + \(9\ x4\)\/389 + \(4\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(2\ x1\)\/159 + \(2\ x2\)\/159 + \(5\ x4\)\/159 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(7\ x2\)\/419 + \(4\ x3\)\/419 + \(10\ x4\)\/419 + \(6\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(54\ x2\)\/3335 + \(32\ x3\)\/3335 + \(81\ x4\)\/3335 + \(48\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/271 + \(9\ x4\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/195 + x2\/39 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \(2\ x6\)\/195 \ \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x3\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(4\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(27\ x2\)\/1207 + \(16\ x3\)\/1207 + \(18\ x4\)\/1207 + \(18\ \ x5\)\/1207 - \(6\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 - \(4\ x5\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(4\ x6\)\/565 \[LessEqual] 1, \(10\ x2\)\/419 + \(6\ x3\)\/419 + \(7\ x4\)\/419 + \(4\ \ x5\)\/419 - \(2\ x6\)\/419 \[LessEqual] 1, \(81\ x2\)\/3335 + \(48\ x3\)\/3335 + \(54\ x4\)\/3335 + \(32\ \ x5\)\/3335 - \(18\ x6\)\/3335 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x4\)\/179 \[LessEqual] 1, \(2\ x1\)\/139 + \(3\ x2\)\/139 + \(2\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(2\ x1\)\/185 + x2\/37 + \(2\ x4\)\/185 + \(2\ x5\)\/185 \[LessEqual] 1, \(6\ x1\)\/391 + \(9\ x2\)\/391 + \(4\ x5\)\/391 + \(6\ \ x6\)\/391 \[LessEqual] 1, \(9\ x2\)\/389 + \(4\ x3\)\/389 + \(6\ x4\)\/389 + \(6\ \ x5\)\/389 - \(2\ x6\)\/389 \[LessEqual] 1, \(9\ x2\)\/271 + \(6\ x4\)\/271 - \(2\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/159 + \(5\ x2\)\/159 + \(2\ x4\)\/159 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x2\)\/245 - \(4\ x5\)\/245 + \(2\ \ x6\)\/245 \[LessEqual] 1, \(2\ x1\)\/245 + \(11\ x2\)\/245 + \(2\ x4\)\/245 - \(4\ \ x5\)\/245 \[LessEqual] 1, \(16\ x1\)\/1207 - \(6\ x2\)\/1207 + \(18\ x3\)\/1207 + \(27\ \ x4\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(48\ x1\)\/3335 - \(18\ x2\)\/3335 + \(32\ x3\)\/3335 + \(81\ \ x4\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(-\(\(6\ x2\)\/85\)\) + \(2\ x4\)\/85 + \(3\ x6\)\/85 \ \[LessEqual] 1, \(-x2\) \[LessEqual] 0, x1\/75 - x2\/225 + x3\/50 + x4\/75 + x6\/50 \[LessEqual] 1, \(32\ x1\)\/3335 - \(18\ x2\)\/3335 + \(48\ x3\)\/3335 + \(54\ \ x4\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, x1\/120 + x3\/48 + x4\/120 + x5\/120 + x6\/48 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x1\)\/109 + \(3\ x4\)\/109 + \(2\ x5\)\/109 \[LessEqual] 1, \(18\ x1\)\/1207 - \(6\ x2\)\/1207 + \(27\ x3\)\/1207 + \(18\ \ x4\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x3\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(2\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(4\ x1\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\/629 + \(6\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, x1\/77 + x3\/77 + \(3\ x4\)\/154 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/419 - \(2\ x2\)\/419 + \(4\ x3\)\/419 + \(10\ \ x4\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(-\(\(2\ x2\)\/271\)\) + \(6\ x4\)\/271 + \(9\ x6\)\/271 \ \[LessEqual] 1, \(2\ x1\)\/135 - \(4\ x2\)\/945 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 + \(2\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(10\ x1\)\/629 + \(4\ x3\)\/629 + \(15\ x4\)\/629 + \(6\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x3\)\/100 + \(3\ x5\)\/100 \[LessEqual] 1, \(6\ x1\)\/389 - \(2\ x2\)\/389 + \(9\ x3\)\/389 + \(6\ \ x4\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(6\ x1\)\/307 + \(9\ x4\)\/307 + \(4\ x5\)\/307 \[LessEqual] 1, x6\/23 \[LessEqual] 1, \(2\ x4\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x3\)\/165 + x4\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x3\)\/397 + \(9\ x4\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/165 + x3\/33 + \(2\ x4\)\/165 \[LessEqual] 1, \(6\ x1\)\/397 + \(9\ x3\)\/397 + \(6\ x4\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/109 + \(2\ x4\)\/109 + \(3\ x5\)\/109 \[LessEqual] 1, x1\/77 + \(3\ x3\)\/154 + x4\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(2\ x5\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/179 - \(4\ x3\)\/179 + \(9\ x4\)\/179 \[LessEqual] 1, \(4\ x2\)\/545 + \(4\ x3\)\/545 + \(6\ x4\)\/545 + \(6\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(4\ x3\)\/777 + \(19\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x4\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(2\ x3\)\/93 + x6\/31 \[LessEqual] 1, \(2\ x1\)\/945 + \(8\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(23\ x5\)\/945 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x3\)\/655 + \(12\ \ x4\)\/655 + \(3\ x5\)\/131 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x3\)\/265 - \(4\ x4\)\/265 + \(2\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/179 + \(9\ x3\)\/179 - \(4\ x4\)\/179 \[LessEqual] 1, \(6\ x1\)\/307 + \(4\ x4\)\/307 + \(9\ x5\)\/307 \[LessEqual] 1, \(2\ x1\)\/179 - \(4\ x2\)\/179 + \(9\ x5\)\/179 \[LessEqual] 1, \(2\ x1\)\/265 - \(4\ x2\)\/265 + \(2\ x3\)\/265 + \(11\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x3\)\/545 + \(4\ x4\)\/545 + \(3\ \ x5\)\/109 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x3\)\/565 + \(4\ x4\)\/565 + \(3\ \ x5\)\/113 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(6\ x3\)\/545 + \(4\ x4\)\/545 + \(3\ \ x5\)\/109 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/1015 + \(4\ x2\)\/1015 + \(2\ x3\)\/145 + \(2\ x4\)\ \/203 + \(2\ x5\)\/203 + \(5\ x6\)\/203 \[LessEqual] 1, x1\/75 + x3\/75 + x4\/50 - x5\/225 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x4\/48 + x6\/48 \[LessEqual] 1, \(2\ x1\)\/145 + \(4\ x2\)\/1015 + \(4\ x3\)\/1015 + \(5\ x4\)\ \/203 + \(2\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(48\ x1\)\/3335 + \(81\ x3\)\/3335 + \(32\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/419 + \(10\ x3\)\/419 + \(4\ x4\)\/419 - \(2\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(16\ x1\)\/1207 + \(27\ x3\)\/1207 + \(18\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(-\(\(2\ x3\)\/271\)\) + \(6\ x5\)\/271 + \(9\ x6\)\/271 \ \[LessEqual] 1, \(-\(\(6\ x3\)\/85\)\) + \(2\ x5\)\/85 + \(3\ x6\)\/85 \ \[LessEqual] 1, \(32\ x1\)\/3335 + \(48\ x2\)\/3335 - \(18\ x3\)\/3335 + \(54\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ \ x4\)\/777 + \(19\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(2\ x1\)\/265 + \(2\ x2\)\/265 - \(4\ x3\)\/265 + \(11\ \ x4\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(6\ x1\)\/565 + \(6\ x2\)\/565 + \(3\ x4\)\/113 + \(4\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(4\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x4\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(4\ x5\)\/1015 + \(5\ x6\)\/203 \[LessEqual] 1, \(6\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x4\)\/629 + \(15\ x5\)\/629 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(5\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x4\)\/131 + \(2\ x5\)\/131 \[LessEqual] 1, \(6\ x1\)\/307 + \(4\ x2\)\/307 + \(9\ x3\)\/307 \[LessEqual] 1, \(2\ x1\)\/109 + \(2\ x2\)\/109 + \(3\ x3\)\/109 \[LessEqual] 1, \(6\ x1\)\/565 + \(4\ x2\)\/565 + \(3\ x3\)\/113 + \(6\ \ x5\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x3\)\/109 + \(4\ \ x5\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/545 + \(4\ x2\)\/545 + \(3\ x3\)\/109 + \(6\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(10\ x1\)\/777 + \(4\ x2\)\/777 + \(19\ x3\)\/777 + \(4\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x1\)\/629 + \(6\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/135 + \(2\ x2\)\/945 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 - \(4\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(2\ x1\)\/145 + \(2\ x2\)\/203 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/945 + \(2\ x2\)\/135 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 + \(2\ x5\)\/135 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/629 + \(10\ x2\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\ \/629 + \(6\ x5\)\/629 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x2\)\/131 + \(3\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/145 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(5\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(2\ x6\)\/145 \[LessEqual] 1, \(6\ x1\)\/545 + \(6\ x2\)\/545 + \(3\ x4\)\/109 + \(4\ \ x5\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(4\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x3\)\/629 + \(10\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/203 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/145 + \(5\ x6\)\/203 \[LessEqual] 1, \(6\ x3\)\/271 - \(2\ x5\)\/271 + \(9\ x6\)\/271 \[LessEqual] 1, \(32\ x1\)\/3335 + \(54\ x3\)\/3335 + \(48\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(6\ x2\)\/545 + \(6\ x3\)\/545 + \(4\ x4\)\/545 + \(4\ \ x5\)\/545 + \(3\ x6\)\/109 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x3\)\/1207 + \(27\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x4\)\/131 + \(2\ x6\)\/131 \[LessEqual] 1, \(10\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(5\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(2\ x6\)\/145 \[LessEqual] 1, \(2\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(5\ \ x4\)\/203 + \(2\ x5\)\/145 + \(4\ x6\)\/1015 \[LessEqual] 1, \(10\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x3\)\/389 + \(9\ x4\)\/389 - \(2\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(48\ x1\)\/3335 + \(32\ x2\)\/3335 - \(18\ x3\)\/3335 + \(81\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, x1\/77 + x2\/77 + \(3\ x5\)\/154 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/419 + \(4\ x2\)\/419 - \(2\ x3\)\/419 + \(10\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(16\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x3\)\/1207 + \(27\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(4\ x1\)\/629 + \(10\ x2\)\/629 + \(6\ x4\)\/629 + \(6\ \ x5\)\/629 + \(15\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(10\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x4\)\/629 + \(15\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/135 + \(8\ x2\)\/945 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(23\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(-x3\) \[LessEqual] 0, x1\/75 + x2\/50 - x3\/225 + x5\/75 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/48 + x4\/120 + x5\/120 + x6\/48 \[LessEqual] 1, x1\/75 + x2\/75 - x4\/225 + x5\/50 + x6\/50 \[LessEqual] 1, x1\/120 + x2\/120 + x3\/120 + x5\/48 + x6\/48 \[LessEqual] 1, \(4\ x1\)\/1015 + \(2\ x2\)\/145 + \(4\ x3\)\/1015 + \(2\ x4\)\ \/203 + \(2\ x5\)\/203 + \(5\ x6\)\/203 \[LessEqual] 1, \(2\ x1\)\/145 + \(4\ x2\)\/1015 + \(4\ x3\)\/1015 + \(2\ x4\)\ \/203 + \(5\ x5\)\/203 + \(2\ x6\)\/203 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x4\)\/131 + \(3\ x5\)\/131 \[LessEqual] 1, \(6\ x1\)\/655 + \(12\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(10\ x1\)\/1041 + \(16\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x3\/35 - \(4\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/945 + \(2\ x2\)\/135 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 + \(2\ x5\)\/135 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/629 + \(6\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ \ x4\)\/629 + \(10\ x5\)\/629 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ \ x4\)\/131 + \(12\ x5\)\/655 \[LessEqual] 1, x1\/77 + \(3\ x2\)\/154 + x5\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(2\ x2\)\/93 + x6\/31 \[LessEqual] 1, \(32\ x1\)\/3335 + \(54\ x2\)\/3335 - \(18\ x4\)\/3335 + \(48\ \ x5\)\/3335 + \(81\ x6\)\/3335 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x4\)\/1207 + \(27\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x5\)\/131 + \(2\ x6\)\/131 \[LessEqual] 1, \(6\ x2\)\/271 - \(2\ x4\)\/271 + \(9\ x6\)\/271 \[LessEqual] 1, \(2\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(5\ x5\)\/203 + \(2\ x6\)\/145 \[LessEqual] 1, \(10\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(3\ x3\)\/100 - x4\/50 + \(3\ x5\)\/100 \[LessEqual] 1, \(2\ x3\)\/85 - \(6\ x5\)\/85 + \(3\ x6\)\/85 \[LessEqual] 1, \(-x5\) \[LessEqual] 0, \(3\ x2\)\/100 + \(3\ x4\)\/100 - x5\/50 \[LessEqual] 1, \(18\ x1\)\/1207 + \(27\ x2\)\/1207 - \(6\ x3\)\/1207 + \(18\ \ x5\)\/1207 + \(16\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(2\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x2\)\/165 + x5\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x2\)\/397 + \(9\ x5\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x4\)\/389 + \(9\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(16\ x1\)\/1207 + \(27\ x2\)\/1207 - \(6\ x4\)\/1207 + \(18\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(48\ x1\)\/3335 + \(81\ x2\)\/3335 - \(18\ x4\)\/3335 + \(32\ \ x5\)\/3335 + \(54\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/419 + \(10\ x2\)\/419 - \(2\ x4\)\/419 + \(4\ \ x5\)\/419 + \(7\ x6\)\/419 \[LessEqual] 1, \(-x4\) \[LessEqual] 0, \(2\ x2\)\/85 - \(6\ x4\)\/85 + \(3\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/131 + \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(2\ x1\)\/135 + \(23\ x2\)\/945 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(8\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(10\ x1\)\/629 + \(15\ x2\)\/629 + \(6\ x3\)\/629 + \(4\ x5\)\ \/629 + \(6\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/145 + \(5\ x2\)\/203 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(4\ x5\)\/1015 + \(2\ x6\)\/203 \[LessEqual] 1, \(10\ x1\)\/1041 + \(25\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/945 + \(23\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(8\ x5\)\/945 - \(4\ x6\)\/945 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(12\ x3\)\/655 + \(6\ \ x4\)\/655 + \(4\ x5\)\/655 \[LessEqual] 1, \(6\ x1\)\/389 + \(9\ x2\)\/389 - \(2\ x3\)\/389 + \(6\ \ x5\)\/389 + \(4\ x6\)\/389 \[LessEqual] 1, \(3\ x2\)\/100 - x3\/50 + \(3\ x4\)\/100 \[LessEqual] 1, \(10\ x1\)\/777 + \(19\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ x4\)\ \/777 + \(4\ x5\)\/777 + \(10\ x6\)\/777 \[LessEqual] 1, \(10\ x1\)\/1041 + \(25\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(16\ x6\)\/1041 \[LessEqual] 1, \(2\ x1\)\/203 + \(5\ x2\)\/203 + \(4\ x3\)\/1015 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(2\ x6\)\/145 \[LessEqual] 1, \(2\ x1\)\/109 + \(3\ x2\)\/109 + \(2\ x3\)\/109 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(2\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x5\)\/655 \[LessEqual] 1, \(2\ x1\)\/203 + \(5\ x2\)\/203 + \(2\ x3\)\/145 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(4\ x6\)\/1015 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\ \/629 + \(4\ x5\)\/629 \[LessEqual] 1, \(2\ x1\)\/165 + x2\/33 + \(2\ x5\)\/165 \[LessEqual] 1, \(6\ x1\)\/397 + \(9\ x2\)\/397 + \(6\ x5\)\/397 + \(4\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/265 + \(11\ x2\)\/265 + \(2\ x4\)\/265 - \(4\ \ x5\)\/265 + \(2\ x6\)\/265 \[LessEqual] 1, \(2\ x1\)\/179 + \(9\ x2\)\/179 - \(4\ x5\)\/179 \[LessEqual] 1, \(6\ x1\)\/307 + \(9\ x2\)\/307 + \(4\ x3\)\/307 \[LessEqual] 1, \(6\ x1\)\/545 + \(3\ x2\)\/109 + \(4\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/565 + \(3\ x2\)\/113 + \(4\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x6\)\/565 \[LessEqual] 1, \(6\ x1\)\/545 + \(3\ x2\)\/109 + \(4\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x6\)\/545 \[LessEqual] 1, \(6\ x1\)\/385 - \(6\ x2\)\/385 + \(9\ x3\)\/385 + \(6\ \ x4\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, \(-\(x2\/16\)\) + x3\/32 + x5\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x2\)\/35 + x3\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x4\)\/35 + x5\/35 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x4\)\/385 + \(9\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, x3\/32 - x4\/16 + x5\/32 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x3\)\/385 + \(9\ x4\)\/385 - \(6\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x4\/35 - \(2\ x5\)\/35 \[LessEqual] 1, x2\/32 + x4\/32 - x5\/16 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 \ \[LessEqual] 1, \(6\ x1\)\/385 + \(9\ x2\)\/385 - \(6\ x3\)\/385 + \(6\ \ x5\)\/385 + \(4\ x6\)\/385 \[LessEqual] 1, x2\/32 - x3\/16 + x4\/32 \[LessEqual] 1, \(3\ x1\)\/122 + \(3\ x4\)\/122 + x5\/61 \[LessEqual] 1, x1\/48 + x3\/120 + x4\/48 + x5\/120 + x6\/120 \[LessEqual] 1, \(12\ x1\)\/655 + \(4\ x3\)\/655 + \(3\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/45 + x4\/45 + x5\/45 \[LessEqual] 1, x1\/50 - x2\/225 + x3\/75 + x4\/50 + x6\/75 \[LessEqual] 1, \(3\ x1\)\/167 + \(2\ x3\)\/167 + \(3\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x4\)\/185 + \(2\ x5\)\/185 + x6\/37 \[LessEqual] 1, \(-\(x2\/31\)\) + \(3\ x5\)\/62 + x6\/62 \[LessEqual] 1, \(3\ x1\)\/122 + x4\/61 + \(3\ x5\)\/122 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x3\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, \(18\ x1\)\/1207 - \(6\ x2\)\/1207 + \(16\ x3\)\/1207 + \(18\ \ x4\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(3\ \ x6\)\/139 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x3\)\/167 + \(2\ x4\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, x1\/60 + x3\/60 + x4\/60 + x6\/60 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x3\)\/167 + \(3\ x4\)\/167 + \(2\ \ x6\)\/167 \[LessEqual] 1, \(-\(x2\/31\)\) + x3\/62 + \(3\ x5\)\/62 \[LessEqual] 1, \(2\ x1\)\/135 - \(4\ x2\)\/945 + \(23\ x3\)\/945 + \(8\ \ x4\)\/945 + \(2\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 - \(18\ x2\)\/3335 + \(81\ x3\)\/3335 + \(32\ \ x4\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x3\)\/131 + \(4\ x4\)\/655 + \(6\ \ x5\)\/655 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x3\)\/629 + \(4\ x4\)\/629 + \(6\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(-\(x2\/50\)\) + \(3\ x5\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(-\(x3\/31\)\) + \(3\ x4\)\/62 + x6\/62 \[LessEqual] 1, \(-\(x3\/50\)\) + \(3\ x4\)\/100 + \(3\ x6\)\/100 \[LessEqual] 1, \(6\ x1\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x5\)\/165 + x6\/33 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x4\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/389 - \(2\ x2\)\/389 + \(4\ x3\)\/389 + \(6\ \ x4\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, x1\/51 + x3\/51 + x4\/51 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x3\)\/179 + \(2\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(2\ x1\)\/93 + x3\/31 \[LessEqual] 1, \(6\ x1\)\/271 - \(2\ x2\)\/271 + \(9\ x3\)\/271 \[LessEqual] 1, x1\/50 + x3\/50 + x4\/75 - x5\/225 + x6\/75 \[LessEqual] 1, \(3\ x1\)\/167 + \(2\ x2\)\/167 + \(3\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(12\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x4\)\/655 + \(3\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, \(16\ x1\)\/1041 + \(4\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(25\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, \(16\ x1\)\/1041 + \(4\ x2\)\/1041 + \(4\ x3\)\/1041 + \(25\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/79 - \(2\ x3\)\/79 + \(4\ x4\)\/79 \[LessEqual] 1, \(2\ x1\)\/93 + x4\/31 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x3\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, x1\/79 + \(4\ x3\)\/79 - \(2\ x4\)\/79 \[LessEqual] 1, \(3\ x1\)\/122 + x2\/61 + \(3\ x3\)\/122 \[LessEqual] 1, x1\/48 + x2\/120 + x3\/48 + x4\/120 + x6\/120 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x3\)\/1207 + \(16\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, x1\/48 + x2\/120 + x4\/120 + x5\/48 + x6\/120 \[LessEqual] 1, x1\/50 + x2\/75 - x3\/225 + x5\/50 + x6\/75 \[LessEqual] 1, \(18\ x1\)\/1207 + \(16\ x2\)\/1207 - \(6\ x3\)\/1207 + \(18\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(2\ x1\)\/139 + \(2\ x2\)\/139 + \(2\ x5\)\/139 + \(3\ \ x6\)\/139 \[LessEqual] 1, \(6\ x1\)\/389 + \(4\ x2\)\/389 - \(2\ x3\)\/389 + \(6\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(6\ x1\)\/397 + \(4\ x2\)\/397 + \(6\ x5\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, \(6\ x1\)\/655 + \(2\ x2\)\/131 + \(6\ x4\)\/655 + \(6\ \ x5\)\/655 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/79 - \(2\ x2\)\/79 + \(4\ x5\)\/79 \[LessEqual] 1, \(18\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x4\)\/1207 + \(16\ \ x5\)\/1207 + \(27\ x6\)\/1207 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x5\)\/131 + \(3\ x6\)\/131 \[LessEqual] 1, \(2\ x1\)\/185 + \(2\ x2\)\/185 + \(2\ x3\)\/185 + x6\/37 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x3\)\/179 + \(5\ x5\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/180 + x4\/180 + x5\/45 + x6\/72 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(6\ x3\)\/655 + \(2\ \ x4\)\/131 + \(3\ x6\)\/131 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/180 + x4\/45 + x5\/180 + x6\/72 \[LessEqual] 1, \(2\ x1\)\/179 + \(2\ x2\)\/179 + \(5\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, \(3\ x3\)\/100 - x4\/50 + \(3\ x6\)\/100 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x3\)\/389 + \(4\ x4\)\/389 - \(2\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(3\ x3\)\/62 - x4\/31 + x6\/62 \[LessEqual] 1, \(3\ x3\)\/62 - x4\/31 + x5\/62 \[LessEqual] 1, \(12\ x1\)\/655 + \(6\ x2\)\/655 + \(3\ x3\)\/131 + \(4\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/72 + x2\/180 + x3\/45 + x4\/180 + x5\/180 + x6\/72 \[LessEqual] 1, \(16\ x1\)\/1041 + \(10\ x2\)\/1041 + \(25\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x3\/34 + x5\/34 - x6\/17 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + x5\/35 - \(4\ x6\)\/175 \[LessEqual] 1, \(4\ x2\)\/385 + \(9\ x3\)\/385 + \(6\ x4\)\/385 + \(6\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + x3\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 - \(2\ x6\)\/35 \ \[LessEqual] 1, \(3\ x3\)\/85 + \(2\ x5\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 - \(4\ x6\)\/175 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x3\)\/100 - x6\/50 \[LessEqual] 1, x1\/32 + x3\/32 - x6\/16 \[LessEqual] 1, x1\/49 + x3\/49 + x4\/49 - \(2\ x6\)\/49 \[LessEqual] 1, \(2\ x1\)\/135 + \(2\ x2\)\/945 + \(8\ x3\)\/945 + \(23\ \ x4\)\/945 - \(4\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(32\ x3\)\/3335 + \(81\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(6\ x2\)\/655 + \(4\ x3\)\/655 + \(3\ \ x4\)\/131 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(6\ x2\)\/629 + \(4\ x3\)\/629 + \(15\ \ x4\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(6\ x1\)\/271 + \(9\ x4\)\/271 - \(2\ x5\)\/271 \[LessEqual] 1, x1\/60 + x2\/60 + x5\/60 + x6\/60 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x2\)\/167 + \(2\ x5\)\/167 + \(3\ \ x6\)\/167 \[LessEqual] 1, \(3\ x1\)\/167 + \(3\ x2\)\/167 + \(3\ x5\)\/167 + \(2\ \ x6\)\/167 \[LessEqual] 1, \(2\ x1\)\/93 + x5\/31 \[LessEqual] 1, \(2\ x1\)\/135 + \(8\ x2\)\/945 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(23\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(32\ x2\)\/3335 - \(18\ x4\)\/3335 + \(81\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(4\ x2\)\/655 + \(6\ x3\)\/655 + \(3\ \ x5\)\/131 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(4\ x2\)\/629 + \(6\ x3\)\/629 + \(15\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(6\ x1\)\/271 - \(2\ x4\)\/271 + \(9\ x5\)\/271 \[LessEqual] 1, x1\/45 + x2\/45 + x3\/45 \[LessEqual] 1, \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(4\ x4\)\/385 + \(9\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x3\)\/85 + \(3\ x5\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x5\/35 - \(2\ x6\)\/35 \[LessEqual] 1, x1\/32 + x5\/32 - x6\/16 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x5\)\/100 - x6\/50 \[LessEqual] 1, \(-x6\) \[LessEqual] 0, x1\/32 + x4\/32 - x6\/16 \[LessEqual] 1, \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(9\ x4\)\/385 + \(4\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + x4\/35 - \(2\ x6\)\/35 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x4\)\/100 - x6\/50 \[LessEqual] 1, \(2\ x1\)\/165 + \(2\ x2\)\/165 + x6\/33 \[LessEqual] 1, \(6\ x1\)\/397 + \(6\ x2\)\/397 + \(4\ x5\)\/397 + \(9\ \ x6\)\/397 \[LessEqual] 1, x1\/51 + x2\/51 + x5\/51 \[LessEqual] 1, \(6\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x4\)\/389 + \(4\ \ x5\)\/389 + \(9\ x6\)\/389 \[LessEqual] 1, \(3\ x2\)\/100 - x5\/50 + \(3\ x6\)\/100 \[LessEqual] 1, x1\/48 + x2\/48 + x3\/120 + x5\/120 + x6\/120 \[LessEqual] 1, x2\/62 - x3\/31 + \(3\ x4\)\/62 \[LessEqual] 1, x1\/50 + x2\/50 - x4\/225 + x5\/75 + x6\/75 \[LessEqual] 1, \(3\ x2\)\/62 - x5\/31 + x6\/62 \[LessEqual] 1, \(3\ x2\)\/62 + x4\/62 - x5\/31 \[LessEqual] 1, \(12\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x3\)\/655 + \(4\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(3\ x1\)\/122 + \(3\ x2\)\/122 + x3\/61 \[LessEqual] 1, x1\/72 + x2\/45 + x3\/180 + x4\/180 + x5\/180 + x6\/72 \[LessEqual] 1, \(16\ x1\)\/1041 + \(25\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(10\ x6\)\/1041 \[LessEqual] 1, x1\/49 + x2\/49 + x5\/49 - \(2\ x6\)\/49 \[LessEqual] 1, \(9\ x2\)\/385 + \(4\ x3\)\/385 + \(6\ x4\)\/385 + \(6\ \ x5\)\/385 - \(6\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x4\)\/175 + \(2\ x5\)\/175 - \(2\ x6\)\/35 \ \[LessEqual] 1, x1\/32 + x2\/32 - x6\/16 \[LessEqual] 1, \(2\ x2\)\/85 + \(3\ x4\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, \(3\ x2\)\/85 + \(2\ x4\)\/85 - \(6\ x6\)\/85 \[LessEqual] 1, x2\/34 + x4\/34 - x6\/17 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x4\/35 + \(2\ x5\)\/175 - \(4\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ x6\)\/175 \ \[LessEqual] 1, \(2\ x1\)\/135 + \(23\ x2\)\/945 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(8\ x5\)\/945 + \(2\ x6\)\/135 \[LessEqual] 1, \(54\ x1\)\/3335 + \(81\ x2\)\/3335 - \(18\ x3\)\/3335 + \(32\ \ x5\)\/3335 + \(48\ x6\)\/3335 \[LessEqual] 1, \(6\ x1\)\/655 + \(3\ x2\)\/131 + \(6\ x4\)\/655 + \(4\ \ x5\)\/655 + \(12\ x6\)\/655 \[LessEqual] 1, \(6\ x1\)\/629 + \(15\ x2\)\/629 + \(6\ x4\)\/629 + \(4\ \ x5\)\/629 + \(10\ x6\)\/629 \[LessEqual] 1, \(2\ x1\)\/179 + \(5\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ \ x6\)\/179 \[LessEqual] 1, x1\/79 + \(4\ x2\)\/79 - \(2\ x5\)\/79 \[LessEqual] 1, \(2\ x1\)\/93 + x2\/31 \[LessEqual] 1, \(6\ x1\)\/271 + \(9\ x2\)\/271 - \(2\ x3\)\/271 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x2\)\/100 - x6\/50 \[LessEqual] 1, x1\/94 - x2\/47 + \(2\ x5\)\/47 + x6\/94 \[LessEqual] 1, \(-\(x2\/16\)\) + x5\/32 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x2\)\/35 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x3\/77 + x4\/77 + \(3\ x6\)\/154 \[LessEqual] 1, \(6\ x1\)\/385 - \(6\ x2\)\/385 + \(4\ x3\)\/385 + \(6\ \ x4\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, x1\/94 - x2\/47 + x3\/94 + \(2\ x5\)\/47 \[LessEqual] 1, \(2\ x1\)\/175 - \(4\ x2\)\/175 + x3\/35 + \(2\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 - \(6\ x2\)\/85 + \(3\ x3\)\/85 \[LessEqual] 1, x1\/51 + x5\/51 + x6\/51 \[LessEqual] 1, x1\/38 + x6\/38 \[LessEqual] 1, x1\/36 + x3\/36 \[LessEqual] 1, x1\/51 + x3\/51 + x5\/51 \[LessEqual] 1, x1\/51 + x4\/51 + x6\/51 \[LessEqual] 1, x1\/51 + x3\/51 + x6\/51 \[LessEqual] 1, x1\/94 + \(2\ x3\)\/47 - x4\/47 + x6\/94 \[LessEqual] 1, \(7\ x1\)\/419 - \(2\ x2\)\/419 + \(10\ x3\)\/419 + \(4\ \ x4\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, x1\/94 + \(2\ x3\)\/47 - x4\/47 + x5\/94 \[LessEqual] 1, \(3\ x1\)\/154 + \(3\ x3\)\/154 + x4\/77 + x6\/77 \[LessEqual] 1, \(2\ x1\)\/47 + x3\/94 + x5\/94 - x6\/47 \[LessEqual] 1, \(3\ x1\)\/62 + x3\/62 - x6\/31 \[LessEqual] 1, \(2\ x1\)\/47 + x3\/94 + x4\/94 - x6\/47 \[LessEqual] 1, x1\/36 + x4\/36 \[LessEqual] 1, x1\/94 - x3\/47 + \(2\ x4\)\/47 + x6\/94 \[LessEqual] 1, \(-\(x3\/16\)\) + x4\/32 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ \ x5\)\/175 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x2\/77 + x5\/77 + \(3\ x6\)\/154 \[LessEqual] 1, x1\/36 + x5\/36 \[LessEqual] 1, x1\/54 + x2\/135 + x3\/135 + x4\/135 + x5\/135 + x6\/54 \[LessEqual] 1, x1\/15 - \(2\ x6\)\/45 \[LessEqual] 1, x1\/63 + \(2\ x2\)\/315 + x3\/63 + \(2\ x4\)\/315 + x5\/63 + \(2\ x6\)\/315 \[LessEqual] 1, x1\/45 + x2\/180 + x3\/72 + x4\/72 + x5\/180 + x6\/180 \[LessEqual] 1, \(6\ x1\)\/385 + \(4\ x2\)\/385 - \(6\ x3\)\/385 + \(6\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, x3\/32 - x4\/16 + x6\/32 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x4\)\/385 + \(4\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x4\)\/35 + x6\/35 \[LessEqual] 1, \(7\ x1\)\/419 + \(4\ x2\)\/419 - \(2\ x4\)\/419 + \(10\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/62 + x5\/62 - x6\/31 \[LessEqual] 1, \(3\ x1\)\/62 + x4\/62 - x6\/31 \[LessEqual] 1, \(6\ x1\)\/385 + \(6\ x3\)\/385 + \(4\ x4\)\/385 - \(6\ \ x5\)\/385 + \(9\ x6\)\/385 \[LessEqual] 1, \(7\ x1\)\/419 + \(4\ x3\)\/419 + \(10\ x4\)\/419 - \(2\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/154 + x3\/77 + \(3\ x4\)\/154 + x6\/77 \[LessEqual] 1, x1\/51 + x2\/51 + x6\/51 \[LessEqual] 1, x2\/32 - x5\/16 + x6\/32 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(2\ \ x5\)\/35 + x6\/35 \[LessEqual] 1, \(3\ x1\)\/154 + x2\/77 + \(3\ x5\)\/154 + x6\/77 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + x5\/35 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 - \(6\ x4\)\/85 + \(3\ x5\)\/85 \[LessEqual] 1, x1\/45 + x2\/72 + x3\/180 + x4\/180 + x5\/72 + x6\/180 \[LessEqual] 1, x1\/39 + \(2\ x2\)\/195 + \(2\ x3\)\/195 + \(2\ x4\)\/195 + \ \(2\ x5\)\/195 \[LessEqual] 1, x1\/94 + x2\/94 - x3\/47 + \(2\ x4\)\/47 \[LessEqual] 1, x1\/51 + x2\/51 + x4\/51 \[LessEqual] 1, \(2\ x1\)\/47 + x2\/94 + x5\/94 - x6\/47 \[LessEqual] 1, x1\/94 + \(2\ x2\)\/47 - x5\/47 + x6\/94 \[LessEqual] 1, x1\/94 + \(2\ x2\)\/47 + x4\/94 - x5\/47 \[LessEqual] 1, \(2\ x1\)\/47 + x2\/94 + x4\/94 - x6\/47 \[LessEqual] 1, x1\/63 + x2\/63 + \(2\ x3\)\/315 + x4\/63 + \(2\ x5\)\/315 + \(2\ x6\)\/315 \[LessEqual] 1, \(2\ x1\)\/85 + \(3\ x4\)\/85 - \(6\ x5\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + \(2\ x2\)\/175 + x4\/35 - \(4\ x5\)\/175 + \(2\ x6\)\/175 \[LessEqual] 1, \(2\ x1\)\/85 + \(3\ x2\)\/85 - \(6\ x3\)\/85 \[LessEqual] 1, \(2\ x1\)\/175 + x2\/35 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x6\)\/175 \ \[LessEqual] 1, \(3\ x1\)\/62 + x2\/62 - x6\/31 \[LessEqual] 1, x1\/36 + x2\/36 \[LessEqual] 1, \(3\ x1\)\/154 + \(3\ x2\)\/154 + x5\/77 + x6\/77 \[LessEqual] 1, \(7\ x1\)\/419 + \(10\ x2\)\/419 - \(2\ x3\)\/419 + \(4\ \ x5\)\/419 + \(6\ x6\)\/419 \[LessEqual] 1, x1\/49 - \(2\ x2\)\/49 + x5\/49 + x6\/49 \[LessEqual] 1, x1\/62 - x2\/31 + \(3\ x5\)\/62 \[LessEqual] 1, x1\/32 - x2\/16 + x5\/32 \[LessEqual] 1, \(9\ x1\)\/385 - \(6\ x2\)\/385 + \(6\ x3\)\/385 + \(4\ \ x4\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/35 - \(2\ x2\)\/35 + \(2\ x3\)\/175 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(3\ x1\)\/85 - \(6\ x2\)\/85 + \(2\ x3\)\/85 \[LessEqual] 1, x1\/34 - x2\/17 + x3\/34 \[LessEqual] 1, x1\/35 - \(4\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x3\)\/179 + \(2\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(27\ x1\)\/1207 - \(6\ x2\)\/1207 + \(18\ x3\)\/1207 + \(16\ \ x4\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x3\)\/655 + \(2\ x4\)\/131 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(81\ x1\)\/3335 - \(18\ x2\)\/3335 + \(54\ x3\)\/3335 + \(48\ \ x4\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/419 - \(2\ x2\)\/419 + \(7\ x3\)\/419 + \(6\ \ x4\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x3\)\/655 + \(12\ x4\)\/655 + \(6\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x3\)\/629 + \(10\ x4\)\/629 + \(6\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(23\ x1\)\/945 - \(4\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 + \(2\ x5\)\/945 + \(8\ x6\)\/945 \[LessEqual] 1, x1\/62 + \(3\ x3\)\/62 - x4\/31 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x3\)\/265 + \(2\ x4\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(4\ x1\)\/79 + x3\/79 - \(2\ x6\)\/79 \[LessEqual] 1, x1\/49 - \(2\ x3\)\/49 + x4\/49 + x6\/49 \[LessEqual] 1, x1\/49 + x3\/49 - \(2\ x4\)\/49 + x6\/49 \[LessEqual] 1, x1\/34 - x4\/17 + x5\/34 \[LessEqual] 1, \(4\ x1\)\/79 + x5\/79 - \(2\ x6\)\/79 \[LessEqual] 1, \(4\ x1\)\/79 + x4\/79 - \(2\ x6\)\/79 \[LessEqual] 1, \(3\ x1\)\/113 + \(4\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(25\ x1\)\/1041 + \(4\ x2\)\/1041 + \(10\ x3\)\/1041 + \(16\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(5\ x1\)\/203 + \(4\ x2\)\/1015 + \(2\ x3\)\/203 + \(2\ \ x4\)\/145 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, x1\/62 - x3\/31 + \(3\ x4\)\/62 \[LessEqual] 1, x1\/32 - x3\/16 + x4\/32 \[LessEqual] 1, \(10\ x1\)\/419 + \(6\ x3\)\/419 + \(7\ x4\)\/419 - \(2\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, x1\/34 + x4\/34 - x5\/17 \[LessEqual] 1, \(9\ x1\)\/385 + \(6\ x2\)\/385 - \(6\ x3\)\/385 + \(4\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 - \(2\ x3\)\/35 + \(2\ x4\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(27\ x1\)\/1207 + \(18\ x2\)\/1207 - \(6\ x3\)\/1207 + \(16\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(2\ \ x5\)\/131 + \(6\ x6\)\/655 \[LessEqual] 1, x1\/49 + x2\/49 - \(2\ x5\)\/49 + x6\/49 \[LessEqual] 1, \(10\ x1\)\/419 + \(6\ x2\)\/419 - \(2\ x4\)\/419 + \(7\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, \(25\ x1\)\/1041 + \(10\ x2\)\/1041 + \(4\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(16\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, x1\/35 + \(2\ x3\)\/175 - \(2\ x4\)\/35 + \(2\ x5\)\/175 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(27\ x1\)\/1207 + \(16\ x2\)\/1207 - \(6\ x4\)\/1207 + \(18\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(3\ x1\)\/131 + \(2\ x2\)\/131 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(9\ x1\)\/385 + \(4\ x2\)\/385 - \(6\ x4\)\/385 + \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, x1\/32 + x3\/32 - x4\/16 \[LessEqual] 1, \(3\ x1\)\/131 + \(12\ x2\)\/655 + \(6\ x3\)\/655 + \(6\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(15\ x1\)\/629 + \(10\ x2\)\/629 + \(6\ x3\)\/629 + \(6\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(3\ x1\)\/85 - \(6\ x4\)\/85 + \(2\ x5\)\/85 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x3\)\/175 - \(4\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/135 + \(2\ x3\)\/945 - \(4\ \ x4\)\/945 + \(2\ x5\)\/135 + \(8\ x6\)\/945 \[LessEqual] 1, \(81\ x1\)\/3335 + \(48\ x2\)\/3335 - \(18\ x4\)\/3335 + \(54\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(4\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/145 + \(2\ x3\)\/203 + \(4\ \ x4\)\/1015 + \(2\ x5\)\/203 + \(4\ x6\)\/1015 \[LessEqual] 1, \(25\ x1\)\/1041 + \(16\ x2\)\/1041 + \(10\ x3\)\/1041 + \(4\ \ x4\)\/1041 + \(10\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x4\)\/175 - \(2\ x5\)\/35 + \(2\ \ x6\)\/175 \[LessEqual] 1, \(9\ x1\)\/385 + \(4\ x3\)\/385 + \(6\ x4\)\/385 - \(6\ \ x5\)\/385 + \(6\ x6\)\/385 \[LessEqual] 1, \(27\ x1\)\/1207 + \(16\ x3\)\/1207 + \(18\ x4\)\/1207 - \(6\ \ x5\)\/1207 + \(18\ x6\)\/1207 \[LessEqual] 1, \(25\ x1\)\/1041 + \(10\ x2\)\/1041 + \(16\ x3\)\/1041 + \(10\ \ x4\)\/1041 + \(4\ x5\)\/1041 + \(4\ x6\)\/1041 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(12\ x3\)\/655 + \(6\ \ x4\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(81\ x1\)\/3335 + \(48\ x3\)\/3335 + \(54\ x4\)\/3335 - \(18\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/945 + \(2\ x3\)\/135 + \(2\ \ x4\)\/135 - \(4\ x5\)\/945 + \(8\ x6\)\/945 \[LessEqual] 1, \(3\ x1\)\/85 + \(2\ x4\)\/85 - \(6\ x5\)\/85 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 + \(2\ x3\)\/175 + \(2\ x4\)\/175 - \(4\ x5\ \)\/175 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x3\)\/265 + \(2\ \ x4\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(6\ x3\)\/565 + \(6\ \ x4\)\/565 + \(4\ x5\)\/565 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x3\)\/179 + \(2\ \ x4\)\/179 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(6\ x4\)\/655 + \(12\ \ x5\)\/655 + \(4\ x6\)\/655 \[LessEqual] 1, \(11\ x1\)\/265 + \(2\ x2\)\/265 + \(2\ x4\)\/265 + \(2\ \ x5\)\/265 - \(4\ x6\)\/265 \[LessEqual] 1, \(4\ x1\)\/79 + x2\/79 - \(2\ x6\)\/79 \[LessEqual] 1, x1\/62 + \(3\ x2\)\/62 - x5\/31 \[LessEqual] 1, x1\/32 + x2\/32 - x5\/16 \[LessEqual] 1, \(3\ x1\)\/113 + \(6\ x2\)\/565 + \(4\ x3\)\/565 + \(6\ \ x4\)\/565 + \(6\ x5\)\/565 \[LessEqual] 1, \(3\ x1\)\/131 + \(6\ x2\)\/655 + \(2\ x3\)\/131 + \(6\ \ x4\)\/655 + \(6\ x6\)\/655 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/203 + \(4\ x3\)\/1015 + \(2\ \ x4\)\/203 + \(2\ x5\)\/145 + \(4\ x6\)\/1015 \[LessEqual] 1, \(5\ x1\)\/203 + \(2\ x2\)\/203 + \(2\ x3\)\/145 + \(2\ \ x4\)\/203 + \(4\ x5\)\/1015 + \(4\ x6\)\/1015 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x2\)\/629 + \(10\ x3\)\/629 + \(6\ x4\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, \(3\ x1\)\/85 + \(2\ x2\)\/85 - \(6\ x3\)\/85 \[LessEqual] 1, \(81\ x1\)\/3335 + \(54\ x2\)\/3335 - \(18\ x3\)\/3335 + \(48\ \ x5\)\/3335 + \(32\ x6\)\/3335 \[LessEqual] 1, \(10\ x1\)\/419 + \(7\ x2\)\/419 - \(2\ x3\)\/419 + \(6\ \ x5\)\/419 + \(4\ x6\)\/419 \[LessEqual] 1, x1\/34 + x2\/34 - x3\/17 \[LessEqual] 1, x1\/35 + \(2\ x2\)\/175 - \(4\ x3\)\/175 + \(2\ x4\)\/175 + \(2\ x5\ \)\/175 \[LessEqual] 1, \(5\ x1\)\/179 + \(2\ x2\)\/179 + \(2\ x4\)\/179 + \(2\ \ x5\)\/179 \[LessEqual] 1, \(23\ x1\)\/945 + \(2\ x2\)\/135 - \(4\ x3\)\/945 + \(2\ \ x4\)\/945 + \(2\ x5\)\/135 + \(8\ x6\)\/945 \[LessEqual] 1, \(15\ x1\)\/629 + \(6\ x2\)\/629 + \(6\ x4\)\/629 + \(10\ x5\)\ \/629 + \(4\ x6\)\/629 \[LessEqual] 1, x1\/37 + \(2\ x3\)\/185 + \(2\ x5\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(3\ x1\)\/100 - x2\/50 + \(3\ x5\)\/100 \[LessEqual] 1, \(5\ x1\)\/159 + \(2\ x3\)\/159 + \(2\ x5\)\/159 \[LessEqual] 1, \(3\ x1\)\/109 + \(2\ x4\)\/109 + \(2\ x5\)\/109 \[LessEqual] 1, \(3\ x1\)\/139 + \(2\ x3\)\/139 + \(2\ x4\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(9\ x1\)\/391 + \(6\ x3\)\/391 + \(6\ x4\)\/391 + \(4\ \ x6\)\/391 \[LessEqual] 1, \(9\ x1\)\/389 - \(2\ x2\)\/389 + \(6\ x3\)\/389 + \(4\ \ x4\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x3\)\/245 + \(2\ x5\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x3\)\/245 + \(2\ x4\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(9\ x1\)\/271 - \(2\ x2\)\/271 + \(6\ x3\)\/271 \[LessEqual] 1, \(19\ x1\)\/777 + \(4\ x2\)\/777 + \(10\ x3\)\/777 + \(10\ \ x4\)\/777 + \(4\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x3\)\/100 - x4\/50 \[LessEqual] 1, \(3\ x1\)\/109 + \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x5\)\/545 \[LessEqual] 1, \(3\ x1\)\/109 + \(4\ x2\)\/545 + \(6\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x5\)\/545 \[LessEqual] 1, x1\/37 + \(2\ x2\)\/185 + \(2\ x4\)\/185 + \(2\ x6\)\/185 \ \[LessEqual] 1, \(3\ x1\)\/100 - x3\/50 + \(3\ x4\)\/100 \[LessEqual] 1, \(3\ x1\)\/139 + \(2\ x2\)\/139 + \(2\ x5\)\/139 + \(2\ \ x6\)\/139 \[LessEqual] 1, \(9\ x1\)\/391 + \(6\ x2\)\/391 + \(6\ x5\)\/391 + \(4\ \ x6\)\/391 \[LessEqual] 1, \(19\ x1\)\/777 + \(10\ x2\)\/777 + \(4\ x3\)\/777 + \(4\ x4\)\ \/777 + \(10\ x5\)\/777 + \(4\ x6\)\/777 \[LessEqual] 1, \(9\ x1\)\/389 + \(4\ x2\)\/389 - \(2\ x4\)\/389 + \(6\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(9\ x1\)\/271 - \(2\ x4\)\/271 + \(6\ x5\)\/271 \[LessEqual] 1, \(5\ x1\)\/159 + \(2\ x2\)\/159 + \(2\ x4\)\/159 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x2\)\/245 + \(2\ x5\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(11\ x1\)\/245 + \(2\ x2\)\/245 + \(2\ x4\)\/245 - \(4\ \ x6\)\/245 \[LessEqual] 1, \(9\ x1\)\/389 + \(6\ x2\)\/389 - \(2\ x3\)\/389 + \(4\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(3\ x1\)\/109 + \(2\ x2\)\/109 + \(2\ x3\)\/109 \[LessEqual] 1, \(3\ x1\)\/109 + \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(4\ \ x4\)\/545 + \(6\ x5\)\/545 \[LessEqual] 1, \(9\ x1\)\/389 + \(4\ x3\)\/389 + \(6\ x4\)\/389 - \(2\ \ x5\)\/389 + \(6\ x6\)\/389 \[LessEqual] 1, \(3\ x1\)\/100 + \(3\ x2\)\/100 - x5\/50 \[LessEqual] 1, \(3\ x1\)\/109 + \(6\ x2\)\/545 + \(4\ x3\)\/545 + \(6\ \ x4\)\/545 + \(4\ x5\)\/545 \[LessEqual] 1, \(9\ x1\)\/271 + \(6\ x4\)\/271 - \(2\ x5\)\/271 \[LessEqual] 1, \(9\ x1\)\/271 + \(6\ x2\)\/271 - \(2\ x3\)\/271 \[LessEqual] 1, \(9\ x1\)\/307 + \(6\ x4\)\/307 + \(4\ x5\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(4\ x3\)\/397 + \(6\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x1\)\/307 + \(4\ x4\)\/307 + \(6\ x5\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(6\ x3\)\/397 + \(4\ x4\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, x1\/33 + \(2\ x5\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/33 + \(2\ x4\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/33 + \(2\ x3\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, x1\/31 + \(2\ x3\)\/93 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x3\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, x1\/31 + \(2\ x5\)\/93 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x5\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x4\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, x1\/23 \[LessEqual] 1, x1\/31 + \(2\ x4\)\/93 \[LessEqual] 1, \(9\ x1\)\/307 + \(4\ x2\)\/307 + \(6\ x3\)\/307 \[LessEqual] 1, \(9\ x1\)\/397 + \(4\ x2\)\/397 + \(6\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, \(9\ x1\)\/397 + \(6\ x2\)\/397 + \(4\ x5\)\/397 + \(6\ \ x6\)\/397 \[LessEqual] 1, x1\/33 + \(2\ x2\)\/165 + \(2\ x6\)\/165 \[LessEqual] 1, \(9\ x1\)\/179 + \(2\ x2\)\/179 - \(4\ x6\)\/179 \[LessEqual] 1, \(9\ x1\)\/307 + \(6\ x2\)\/307 + \(4\ x3\)\/307 \[LessEqual] 1, x1\/31 + \(2\ x2\)\/93 \[LessEqual] 1};\)\)}], "Input", CellOpen->False], Cell["\<\ This is the polytope P1 of section 4.1 and it has 2881 vertices and 964 \ facets. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(Length[acconv]\), "\[IndentingNewLine]", \(Length[acineq]\)}], "Input"], Cell[BoxData[ \(2881\)], "Output"], Cell[BoxData[ \(964\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["The Big Minkowski", "Subsection"], Cell["\<\ In this subsection we find the Minkowski sum P = P1 + P2. Many of the \ computations in this section may take up to 30 minutes or so depending on the \ hardware used. Some are also quite memory intensive. However, the final \ results are contained in the last two cells of the subsection which can be \ executed independently. \ \>", "Text"], Cell["\<\ As described in section 4.1, we will exploit the fact that each facet Fi of P \ can be written as a sum of faces from P1 and P2, i.e. Fi = gi + hi. For our \ purposes it suffices to consider sums where dim(gi) + dim(hi) = 5. We will \ also exploit the S4 symmetry of P1 and P2 by only considering a \ representative gi from each orbit of the S4 action. We will need some \ functions which can compute face lattices of polytopes. The first step is \ computing the facet-vertex relations: \ \>", "Text"], Cell[BoxData[{ \(\(VerticesOfFaces[normals_, mins_, vertices_] := Module[{i = 1, j = 1, inclist = Table[{}, {k, 1, Length[normals]}]}, \[IndentingNewLine]While[ i < Length[normals] + 1, \[IndentingNewLine]j = 1; \[IndentingNewLine]While[ j < Length[vertices] + 1, \[IndentingNewLine]If[ Dot[vertices[\([j]\)], normals[\([i]\)]] \[Equal] mins[\([i]\)], inclist[\([i]\)] = Append[inclist[\([i]\)], j], Null]; \[IndentingNewLine]j = j + 1]; \[IndentingNewLine]i = i + 1;\[IndentingNewLine]]; \[IndentingNewLine]inclist];\)\ \), \ "\[IndentingNewLine]", \(\(FacesOfVertices[inclist_] := Module[{NormalIndices = Table[j, {j, 1, Length[inclist]}]}, Table[Select[NormalIndices, Intersection[inclist[\([#]\)], {i}] \[NotEqual] {} &], {i, 1, Max[Flatten[inclist]]}]];\)\), "\[IndentingNewLine]", \(\(P1normals = \(-Table[{Coefficient[acineq[\([i, 1]\)], x1], Coefficient[acineq[\([i, 1]\)], x2], Coefficient[acineq[\([i, 1]\)], x3], Coefficient[acineq[\([i, 1]\)], x4], Coefficient[acineq[\([i, 1]\)], x5], Coefficient[acineq[\([i, 1]\)], x6]}, {i, 1, Length[acineq]}]\);\)\), "\[IndentingNewLine]", \(\(P1mins = \(-acineq[\([All, 2]\)]\);\)\), "\[IndentingNewLine]", \(\(P2normals = \(-Table[{Coefficient[dzineq[\([i, 1]\)], x1], Coefficient[dzineq[\([i, 1]\)], x2], Coefficient[dzineq[\([i, 1]\)], x3], Coefficient[dzineq[\([i, 1]\)], x4], Coefficient[dzineq[\([i, 1]\)], x5], Coefficient[dzineq[\([i, 1]\)], x6]}, {i, 1, Length[dzineq]}]\);\)\), "\[IndentingNewLine]", \(\(P2mins = \(-dzineq[\([All, 2]\)]\);\)\)}], "Input"], Cell[BoxData[{ \(\(P1voff = VerticesOfFaces[P1normals, P1mins, acconv];\)\), "\[IndentingNewLine]", \(\(P1fofv = FacesOfVertices[P1voff];\)\), "\[IndentingNewLine]", \(\(P2voff = VerticesOfFaces[P2normals, P2mins, dzconv];\)\), "\[IndentingNewLine]", \(\(P2fofv = FacesOfVertices[P2voff];\)\)}], "Input"], Cell[BoxData[{ \(\(P1VIndex = Table[i, {i, 1, Length[P1fofv]}];\)\), "\[IndentingNewLine]", \(\(P1FIndex = Table[i, {i, 1, Length[P1voff]}];\)\), "\[IndentingNewLine]", \(\(P1vlist = Table[{i}, {i, 1, Length[P1fofv]}];\)\), "\[IndentingNewLine]", \(\(P2VIndex = Table[i, {i, 1, Length[P2fofv]}];\)\), "\[IndentingNewLine]", \(\(P2FIndex = Table[i, {i, 1, Length[P2voff]}];\)\), "\[IndentingNewLine]", \(\(P2vlist = Table[{i}, {i, 1, Length[P2fofv]}];\)\)}], "Input"], Cell["We now find the orbit representatives for the vertices of P1", "Text"], Cell[BoxData[{ \(\(s4orbits = {{1, 2, 3, 4, 5, 6}, {1, 3, 2, 5, 4, 6}, {2, 1, 3, 4, 6, 5}, {2, 3, 1, 6, 4, 5}, {3, 1, 2, 5, 6, 4}, {3, 2, 1, 6, 5, 4}, {1, 4, 5, 2, 3, 6}, {1, 5, 4, 3, 2, 6}, {4, 1, 5, 2, 6, 3}, {4, 5, 1, 6, 2, 3}, {5, 1, 4, 3, 6, 2}, {5, 4, 1, 6, 3, 2}, {2, 4, 6, 1, 3, 5}, {2, 6, 4, 3, 1, 5}, {4, 2, 6, 1, 5, 3}, {4, 6, 2, 5, 1, 3}, {6, 2, 4, 3, 5, 1}, {6, 4, 2, 5, 3, 1}, {3, 5, 6, 1, 2, 4}, {3, 6, 5, 2, 1, 4}, {5, 3, 6, 1, 4, 2}, {5, 6, 3, 4, 1, 2}, {6, 3, 5, 2, 4, 1}, {6, 5, 3, 4, 2, 1}};\)\), "\[IndentingNewLine]", \(PermuteAList[alist_, perm_] := Table[alist[\([perm[\([i]\)]]\)], {i, 1, Length[alist]}]; MakePermIndex[alist_] := Table[\(Position[alist, PermuteAList[alist[\([i]\)], s4orbits[\([j]\)]]]\)[\([1, 1]\)], {i, 1, Length[alist]}, {j, 1, Length[s4orbits]}];\)}], "Input"], Cell["\<\ The following evaluation may take a considerable amount of time. \ \>", "Text"], Cell[BoxData[{ \(\(P1perms = MakePermIndex[acconv];\)\), "\[IndentingNewLine]", \(\(P1vreps = GetIndexReps[P1vlist, P1perms];\)\)}], "Input"], Cell[BoxData[{ \(\(PermuteAnIndex[indexlist_, permindex_, permnumber_] := Map[permindex[\([#, permnumber]\)] &, indexlist];\)\), "\[IndentingNewLine]", \(\(IndexOrbit[alist_, pindex_] := Union[Sort[ Map[Sort, Map[PermuteAnIndex[alist, pindex, #] &, Table[i, {i, 1, Length[s4orbits]}]]]]];\)\), "\[IndentingNewLine]", \(\(GetIndexReps[alist_, pindex_] := Module[{replist = {}, remainder = Sort[alist]}, \[IndentingNewLine]While[ remainder \[NotEqual] {}, \[IndentingNewLine]replist = Join[replist, {remainder[\([1]\)]}]; \ \[IndentingNewLine]remainder = Complement[remainder, IndexOrbit[remainder[\([1]\)], pindex]];\[IndentingNewLine]]; \[IndentingNewLine]replist\ \[IndentingNewLine]];\)\)}], "Input"], Cell[BoxData[ \(\(P1VertexReps = GetIndexReps[P1vlist, P1perms];\)\)], "Input"], Cell["\<\ With the vertex representatives in hand, we will use the functions below to \ find representatives of the edges, and so on. To do this we consider every \ pair consisting of a representative face and any other face. The set of all \ facets which contain both faces is computed, and then the common vertices of \ those facets are found. The minimal sets under inclusion are the vertex sets \ of faces of the next higher dimension. \ \>", "Text"], Cell[BoxData[{ \(\(Closure[vertices_, voff_, fofv_] := Module[{vs, fs}, \[IndentingNewLine]fs = Fold[Intersection, fofv[\([vertices[\([1]\)]]\)], Map[fofv[\([#]\)] &, vertices]]; \[IndentingNewLine]If[ fs \[NotEqual] {}, vs = Fold[Intersection, voff[\([fs[\([1]\)]]\)], Map[voff[\([#]\)] &, fs]], vs = {}]; \[IndentingNewLine]vs\[IndentingNewLine]];\)\ \ \n\ \ \[IndentingNewLine]\), "\n", \(AddOn[subfacevertices_, vertlist_] := Map[Union[subfacevertices, {#}] &, Complement[vertlist, subfacevertices]]; MinInclusiveSort[alist_, vertlist_] := Module[{mins = {}, \ remainder = alist}, \[IndentingNewLine]remainder = Sort[Complement[alist, {{}}]]; \[IndentingNewLine]While[ remainder \[NotEqual] {}, \[IndentingNewLine]mins = Join[mins, {remainder[\([1]\)]}]; \[IndentingNewLine]remainder = Sort[Select[remainder, Length[Intersection[#, remainder[\([1]\)]]] != Length[remainder[\([1]\)]] &]];\[IndentingNewLine]]; \ \[IndentingNewLine]mins\[IndentingNewLine]];\), "\[IndentingNewLine]", \(\(LatticeStep[subfaces_, vertices_, voff_, fofv_] := Module[{candids, closedcandids}, \[IndentingNewLine]candids = Union[Flatten[Map[AddOn[#, vertices] &, subfaces], 1]]; \[IndentingNewLine]closedcandids = Union[Map[Closure[#, voff, fofv] &, candids]]; \[IndentingNewLine]MinInclusiveSort[closedcandids, verticesvertices]\[IndentingNewLine]];\)\)}], "Input"], Cell[BoxData[{ \(\(P1EdgeRepsWithExtras = LatticeStep[P1VertexReps, P1VIndex, P1voff, P1fofv];\)\), "\[IndentingNewLine]", \(\(P1EdgeReps = GetIndexReps[P1EdgeRepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1EdgeReps]\)}], "Input"], Cell["\<\ For the higher dimenionsal faces of P1, we split the computation into pieces \ to avoid excessive memory usage. \ \>", "Text"], Cell[BoxData[{ \(\(P1EdgeRepsTablePartA = Partition[P1EdgeReps, 100];\)\), "\[IndentingNewLine]", \(\(P1EdgeRepsTable = Join[P1EdgeRepsTablePartA, {Complement[P1EdgeReps, Flatten[P1EdgeRepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1EdgeRepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsWithExtras = Union[Flatten[P1dim2RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim2Reps = GetIndexReps[P1dim2RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim2Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim2RepsTablePartA = Partition[P1dim2Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim2RepsTable = Join[P1dim2RepsTablePartA, {Complement[P1dim2Reps, Flatten[P1dim2RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim2RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsWithExtras = Union[Flatten[P1dim3RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim3Reps = GetIndexReps[P1dim3RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim3Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim3RepsTablePartA = Partition[P1dim3Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim3RepsTable = Join[P1dim3RepsTablePartA, {Complement[P1dim3Reps, Flatten[P1dim3RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim3RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsWithExtras = Union[Flatten[P1dim4RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim4Reps = GetIndexReps[P1dim4RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim4Reps]\)}], "Input"], Cell["\<\ Although unnecessary, its a nice check of our calculations to compute the \ facets of P1 from \"below\" and compare to the Porta output: \ \>", "Text"], Cell[BoxData[{ \(\(P1dim4RepsTablePartA = Partition[P1dim4Reps, 100];\)\), "\[IndentingNewLine]", \(\(P1dim4RepsTable = Join[P1dim4RepsTablePartA, {Complement[P1dim4Reps, Flatten[P1dim4RepsTablePartA, 1]]}];\)\), "\[IndentingNewLine]", \(\(P1dim5RepsWithExtrasTable = Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, P1dim4RepsTable];\)\), "\[IndentingNewLine]", \(\(P1dim5RepsWithExtras = Union[Flatten[P1dim5RepsWithExtrasTable, 1]];\)\), "\[IndentingNewLine]", \(\(P1dim5Reps = GetIndexReps[P1dim5RepsWithExtras, P1perms];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim5Reps]\)}], "Input"], Cell[BoxData[{ \(\(P1dim5Faces = Union[Flatten[Map[IndexOrbit[#, P1perms] &, P1dim5Reps], 1]];\)\), "\[IndentingNewLine]", \(Dimensions[P1dim5Faces]\)}], "Input"], Cell["Next we find all the faces of P2.", "Text"], Cell[BoxData[{ \(\(dzEdges = LatticeStep[P2vlist, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dzEdges = Union[dzEdges];\)\), "\[IndentingNewLine]", \(Dimensions[dzEdges]\)}], "Input"], Cell[BoxData[{ \(\(dz2dims = LatticeStep[dzEdges, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz2dims = Union[dz2dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz2dims]\)}], "Input"], Cell[BoxData[{ \(\(dz3dims = LatticeStep[dz2dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz3dims = Union[dz3dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz3dims]\)}], "Input"], Cell[BoxData[{ \(\(dz4dims = LatticeStep[dz3dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz4dims = Union[dz4dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz4dims]\)}], "Input"], Cell[BoxData[{ \(\(dz5dims = LatticeStep[dz4dims, P2VIndex, P2voff, P2fofv];\)\), "\[IndentingNewLine]", \(\(dz5dims = Union[dz5dims];\)\), "\[IndentingNewLine]", \(Dimensions[dz5dims]\)}], "Input"], Cell["\<\ Now we compute the normals to combinations of faces from polytopes P1 and P2. \ \>", "Text"], Cell[BoxData[ \(GetVectors[indexlist_, vertices_] := Map[vertices[\([#]\)] - vertices[\([indexlist[\([1]\)]]\)] &, Rest[indexlist]]; Normals[vect1_, vect2_] := NullSpace[Union[vect1, vect2]]; NewNormals[list1_, vertices1_, list2_, vertices2_, fofv1_] := \[IndentingNewLine]Module[{vectlist1, vectlist2, newnormlist = {}, tempnorm}, \[IndentingNewLine]For[i = 1, i < Length[list1] + 1, i = i + 1, \[IndentingNewLine]vectlist1 = GetVectors[list1[\([i]\)], vertices1]; \[IndentingNewLine]For[ j = 1, j < Length[list2] + 1, j = j + 1, \[IndentingNewLine]vectlist2 = GetVectors[list2[\([j]\)], vertices2]; \[IndentingNewLine]tempnorm = Normals[vectlist1, vectlist2]; \[IndentingNewLine]If[ Length[tempnorm] \[Equal] 1, \[IndentingNewLine]\(newnormlist = Join[newnormlist, tempnorm];\)\[IndentingNewLine]];\[IndentingNewLine]];\ \[IndentingNewLine]]; \[IndentingNewLine]newnormlist\[IndentingNewLine]];\)], \ "Input"], Cell[BoxData[{ \(\(Pdim3Anddim2 = Union[NewNormals[P1dim3Reps, acconv, dz2dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim3Anddim2]\)}], "Input"], Cell[BoxData[{ \(\(Pdim2Anddim3 = Union[NewNormals[P1dim2Reps, acconv, dz3dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim2Anddim3]\)}], "Input"], Cell[BoxData[{ \(\(Pdim1Anddim4 = Union[NewNormals[P1EdgeReps, acconv, dz4dims, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim1Anddim4]\)}], "Input"], Cell[BoxData[{ \(\(Pdim4Anddim1 = Union[NewNormals[P1dim4Reps, acconv, dzEdges, dzconv, P1fofv]];\)\), "\[IndentingNewLine]", \(Dimensions[Pdim4Anddim1]\)}], "Input"], Cell["\<\ Now we have a large list of candidate normals. Again we exploit the symmetry \ of P by doing most of our calculations on representatives from each orbit. \ \>", "Text"], Cell[BoxData[ \(\(GetReps[alist_] := Module[{newlist = {}, complist = alist, temp, temporbit}, \[IndentingNewLine]While[ complist \[NotEqual] {}, \[IndentingNewLine]temporbit = Sort[Flatten[ Table[Map[ PermuteAList[#, s4orbits[\([i]\)]] &, {complist[\([1]\)]}], {i, 1, Length[s4orbits]}], 1]]; \[IndentingNewLine]temp = temporbit[\([1]\)]; \[IndentingNewLine]complist = Complement[complist, temporbit]; \[IndentingNewLine]newlist = Join[newlist, {temp}];\[IndentingNewLine]]; \ \[IndentingNewLine]newlist];\)\)], "Input"], Cell["\<\ Our construction does not detect whether the computed normal is outward or \ inward pointing so we add in the negatives of each candidate. \ \>", "Text"], Cell[BoxData[{ \(\(NewNormalCandidates = Union[Pdim3Anddim2, Pdim2Anddim3, Pdim1Anddim4, Pdim4Anddim1];\)\), "\[IndentingNewLine]", \(\(NewNormalCandidateReps = GetReps[NewNormalCandidates];\)\), "\[IndentingNewLine]", \(\(NewNormalCandidateReps = Union[NewNormalCandidateReps, \(-NewNormalCandidateReps\)];\)\ \), "\ \[IndentingNewLine]", \(Dimensions[NewNormalCandidateReps]\)}], "Input"], Cell["\<\ Now we need to determine the true normals of facets from our candidate list. \ To do this we need the vertices of P. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(PVertexCandidates = MinkSum[acconv, dzconv];\)\), "\[IndentingNewLine]", \(Dimensions[PVertexCandidates]\)}], "Input"], Cell[BoxData[ \({134784, 6}\)], "Output"] }, Open ]], Cell["\<\ To cut down on the size of the vertices under consideration, we computed the \ convex hulls of other partial Minkowski sums. For example, we could compute \ P = P1' + P2' where P1' is the convex hull of the Minkowski sum of the first 5 Albouy-Chenciner equations and P2' is the convex hull of the Minkowski sum \ of the 3 Dziobek equations plus the remaining Albouy-Chenciner equation. Any \ candidate vertices of P computed in this way which are lacking a full orbit \ under the S4 action must be spurious and can be deleted. Intersecting \ various such candidate lists whittles down the list considerably. After a \ few such iterations we arrive at the list in the cell below, which is not \ open due to its size. \ \>", "Text"], Cell[BoxData[ \(\(PVertexCandidates2 = {{0, 13, 19, 23, 20, 15}, {0, 13, 19, 23, 20, 21}, {0, 13, 19, 23, 23, 15}, {0, 13, 19, 23, 23, 21}, {0, 13, 21, 23, 20, 13}, {0, 13, 21, 23, 20, 19}, {0, 13, 21, 23, 23, 13}, {0, 13, 21, 23, 23, 19}, {0, 13, 23, 23, 16, 15}, {0, 13, 23, 23, 16, 21}, {0, 13, 23, 23, 19, 15}, {0, 13, 23, 23, 19, 21}, {0, 13, 25, 23, 16, 13}, {0, 13, 25, 23, 16, 19}, {0, 13, 25, 23, 19, 13}, {0, 13, 25, 23, 19, 19}, {0, 16, 16, 20, 23, 15}, {0, 16, 16, 20, 23, 21}, {0, 16, 16, 23, 20, 15}, {0, 16, 16, 23, 20, 21}, {0, 16, 18, 20, 23, 13}, {0, 16, 18, 20, 23, 19}, {0, 16, 19, 20, 25, 13}, {0, 16, 19, 20, 25, 19}, {0, 16, 19, 23, 20, 12}, {0, 16, 19, 23, 20, 15}, {0, 16, 19, 23, 20, 18}, {0, 16, 19, 23, 23, 12}, {0, 16, 19, 23, 23, 15}, {0, 16, 19, 23, 23, 18}, {0, 16, 19, 23, 23, 21}, {0, 16, 19, 25, 17, 13}, {0, 16, 19, 25, 17, 19}, {0, 16, 19, 25, 20, 13}, {0, 16, 19, 25, 20, 19}, {0, 16, 23, 23, 13, 15}, {0, 16, 23, 23, 13, 21}, {0, 16, 23, 23, 16, 12}, {0, 16, 23, 23, 16, 15}, {0, 16, 23, 23, 16, 18}, {0, 16, 23, 23, 19, 12}, {0, 16, 23, 23, 19, 15}, {0, 16, 23, 23, 19, 18}, {0, 16, 23, 23, 19, 21}, {0, 16, 23, 25, 13, 13}, {0, 16, 23, 25, 13, 19}, {0, 16, 23, 25, 16, 13}, {0, 16, 23, 25, 16, 19}, {0, 16, 25, 23, 16, 13}, {0, 16, 25, 23, 16, 19}, {0, 17, 25, 19, 16, 13}, {0, 17, 25, 19, 16, 19}, {0, 18, 16, 23, 20, 13}, {0, 18, 16, 23, 20, 19}, {0, 19, 13, 20, 23, 15}, {0, 19, 13, 20, 23, 21}, {0, 19, 13, 23, 23, 15}, {0, 19, 13, 23, 23, 21}, {0, 19, 16, 17, 25, 13}, {0, 19, 16, 17, 25, 19}, {0, 19, 16, 20, 23, 12}, {0, 19, 16, 20, 23, 15}, {0, 19, 16, 20, 23, 18}, {0, 19, 16, 20, 25, 13}, {0, 19, 16, 20, 25, 19}, {0, 19, 16, 23, 23, 12}, {0, 19, 16, 23, 23, 15}, {0, 19, 16, 23, 23, 18}, {0, 19, 16, 23, 23, 21}, {0, 19, 16, 25, 20, 13}, {0, 19, 16, 25, 20, 19}, {0, 19, 23, 23, 13, 15}, {0, 19, 23, 23, 13, 21}, {0, 19, 23, 23, 16, 12}, {0, 19, 23, 23, 16, 15}, {0, 19, 23, 23, 16, 18}, {0, 19, 23, 23, 16, 21}, {0, 19, 23, 25, 13, 13}, {0, 19, 23, 25, 13, 19}, {0, 20, 23, 16, 16, 15}, {0, 20, 23, 16, 16, 21}, {0, 20, 23, 16, 18, 13}, {0, 20, 23, 16, 18, 19}, {0, 20, 23, 19, 13, 15}, {0, 20, 23, 19, 13, 21}, {0, 20, 23, 19, 16, 12}, {0, 20, 23, 19, 16, 15}, {0, 20, 23, 19, 16, 18}, {0, 20, 23, 21, 13, 13}, {0, 20, 23, 21, 13, 19}, {0, 20, 25, 16, 19, 13}, {0, 20, 25, 16, 19, 19}, {0, 20, 25, 19, 16, 13}, {0, 20, 25, 19, 16, 19}, {0, 21, 13, 20, 23, 13}, {0, 21, 13, 20, 23, 19}, {0, 21, 13, 23, 23, 13}, {0, 21, 13, 23, 23, 19}, {0, 23, 13, 16, 23, 15}, {0, 23, 13, 16, 23, 21}, {0, 23, 13, 19, 23, 15}, {0, 23, 13, 19, 23, 21}, {0, 23, 16, 13, 23, 15}, {0, 23, 16, 13, 23, 21}, {0, 23, 16, 13, 25, 13}, {0, 23, 16, 13, 25, 19}, {0, 23, 16, 16, 23, 12}, {0, 23, 16, 16, 23, 15}, {0, 23, 16, 16, 23, 18}, {0, 23, 16, 16, 25, 13}, {0, 23, 16, 16, 25, 19}, {0, 23, 16, 19, 23, 12}, {0, 23, 16, 19, 23, 15}, {0, 23, 16, 19, 23, 18}, {0, 23, 16, 19, 23, 21}, {0, 23, 19, 13, 23, 15}, {0, 23, 19, 13, 23, 21}, {0, 23, 19, 13, 25, 13}, {0, 23, 19, 13, 25, 19}, {0, 23, 19, 16, 23, 12}, {0, 23, 19, 16, 23, 15}, {0, 23, 19, 16, 23, 18}, {0, 23, 19, 16, 23, 21}, {0, 23, 20, 13, 19, 15}, {0, 23, 20, 13, 19, 21}, {0, 23, 20, 13, 21, 13}, {0, 23, 20, 13, 21, 19}, {0, 23, 20, 16, 16, 15}, {0, 23, 20, 16, 16, 21}, {0, 23, 20, 16, 19, 12}, {0, 23, 20, 16, 19, 15}, {0, 23, 20, 16, 19, 18}, {0, 23, 20, 18, 16, 13}, {0, 23, 20, 18, 16, 19}, {0, 23, 23, 13, 19, 15}, {0, 23, 23, 13, 19, 21}, {0, 23, 23, 13, 21, 13}, {0, 23, 23, 13, 21, 19}, {0, 23, 23, 16, 19, 12}, {0, 23, 23, 16, 19, 15}, {0, 23, 23, 16, 19, 18}, {0, 23, 23, 16, 19, 21}, {0, 23, 23, 19, 13, 15}, {0, 23, 23, 19, 13, 21}, {0, 23, 23, 19, 16, 12}, {0, 23, 23, 19, 16, 15}, {0, 23, 23, 19, 16, 18}, {0, 23, 23, 19, 16, 21}, {0, 23, 23, 21, 13, 13}, {0, 23, 23, 21, 13, 19}, {0, 25, 13, 16, 23, 13}, {0, 25, 13, 16, 23, 19}, {0, 25, 13, 19, 23, 13}, {0, 25, 13, 19, 23, 19}, {0, 25, 16, 16, 23, 13}, {0, 25, 16, 16, 23, 19}, {0, 25, 17, 16, 19, 13}, {0, 25, 17, 16, 19, 19}, {0, 25, 20, 16, 19, 13}, {0, 25, 20, 16, 19, 19}, {0, 25, 20, 19, 16, 13}, {0, 25, 20, 19, 16, 19}, {1, 10, 19, 25, 20, 15}, {1, 10, 19, 25, 20, 21}, {1, 10, 19, 25, 23, 15}, {1, 10, 19, 25, 23, 21}, {1, 10, 21, 25, 20, 13}, {1, 10, 21, 25, 20, 19}, {1, 10, 21, 25, 23, 13}, {1, 10, 21, 25, 23, 19}, {1, 10, 23, 25, 16, 15}, {1, 10, 23, 25, 16, 21}, {1, 10, 23, 25, 19, 15}, {1, 10, 23, 25, 19, 21}, {1, 10, 25, 25, 16, 13}, {1, 10, 25, 25, 16, 19}, {1, 10, 25, 25, 19, 13}, {1, 10, 25, 25, 19, 19}, {1, 13, 16, 22, 23, 15}, {1, 13, 16, 22, 23, 21}, {1, 13, 16, 23, 25, 15}, {1, 13, 16, 23, 25, 21}, {1, 13, 16, 25, 20, 15}, {1, 13, 16, 25, 20, 21}, {1, 13, 18, 22, 23, 13}, {1, 13, 18, 22, 23, 19}, {1, 13, 18, 23, 25, 13}, {1, 13, 18, 23, 25, 19}, {1, 13, 19, 22, 25, 13}, {1, 13, 19, 22, 25, 19}, {1, 13, 19, 25, 20, 12}, {1, 13, 19, 25, 20, 15}, {1, 13, 19, 25, 20, 18}, {1, 13, 19, 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