This is the famous Steiner Roman surface, so named because he invented it in Rome, after a visit to the Colosseum. Unilateral, like the Boy and the Crosscap, it is yet another face of the "projective plane". It has a triple point at the center and six cusp points. Steiner surfaces are generally constructed using recovered Whitney umbrellas. Its equation of the fourth degree is surprisingly simple:
x 2 y 2 + y 2 z 2 + z 2 x 2
- 2 x y z = 0
Polyhedral Version