A Projective Tetrahedral Surface
This Demonstration shows a continuous morphing from a sphere to Steiner's Roman surface (a self-intersecting mapping of the real projective plane into 3D space) to a tetrahedron.[more]
At , the surface is a sphere, which can be identified with the points of the special orthogonal group , which generates 3D rotations. As , the rotation matrices are squared to produce the Roman surface. As , the surface transforms to a tetrahedron, associated with the tetrahedral subgroup of .
The resulting tetrahedron is equivalent to one approximated by a Bezier surface.[less]
The surface is represented by the parametric plot of