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    The figure shows part of the Cayley surface. It is a surface of degree 3, with 4 singular points. These singular points are often called nodes. Near each singular point, the surface is closely approximated by a quadric cone.

    There are 9 lines on the Cayley surface. Six of them join pairs of nodes. Thus, we can view the nodes as vertices of a tetrahedron, and these six lines are the edges of the tetrahedron. The other three lines lie in the tritangent plane, which is discussed on the main Cayley surface page.