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A Projective Tetrahedral Surface

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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.

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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.

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Contributed by: Roger Bagula (March 2016)
Open content licensed under CC BY-NC-SA

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The surface is represented by the parametric plot of

,

,

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