Cayley's nodal cubic surface

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 nodal surface in 3-dimensional projective space with four conical points. It can be given by the equation

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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