Steiner’s Roman surface

Send each point (x, y, z) of a sphere to (yz, xz, xy). Opposite points land on the same spot, so the sphere folds into a model of the projective plane with four lobes and six pinch points. The animation runs that map from the sphere and back.

(x, y, z) ↦ (yz, xz, xy)

On mathcurve.com as Surface romaine