Cayley's nodal cubic surface

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Not to be confused with Cayley's ruled cubic surface.
Real points of the Cayley surface

In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic 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.


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