Cayley's nodal cubic surface

Not to be confused with Cayley's ruled cubic surface.

File:CayleyCubic.png

Real points of the Cayley surface

In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic nodal surface in 3-dimensional projective space with four conical points. It can be given by the equation

$wxy+ xyz+ yzw+zwx =0\$

when the four singular points are those with three vanishing coordinates. Changing variables gives several other simple equations defining the Cayley surface.

External links

• Surface de Cayley
• Weisstein, Eric W., "Cayley cubic", MathWorld.