Cayley's Cubic Surface with 4 Singularities

Cayley's cubic surface is one of the most famous cubic surfaces of all: It is the one with the maximum possible number of singularities (four). Moreover, it was Felix Klein who presented a model of it in 1872 to his Göttingen fellow scientists.

Our version is extremely fragile: We tried to make the surface and the singularities as thin as possible in order to make the singularities as thin as possible (ideally, of course, they should only be points). In contrast to the Clebsch Diagonal Cubic with its 27 lines this one has only 9 lines.