Cayley's ruled cubic surface
# Cayley's ruled cubic surface

In differential geometry, Cayley's ruled cubic surface is the ruled cubic surface

    $x^{3}+(4x\,z+y)x=0.\$

It contains a nodal line of self-intersection and two cuspital points at infinity.

In projective coordinates it is $x^{3}+(4x\,z+y\,w)x=0.\$.

