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Regular Polytopes

Russell Towle
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The "Regular Polytopes" notebook constructs all sixteen regular polytopes in four-dimensional space, as well as eleven semi-regular 4-polytopes. It also provides constructions for the regular simplexes, cross polytopes, and hypercubes, in n-dimensional space.

Methods are provided to make both solid and plane projections. Animations are made of the solid sections of the six regular convex 4-polytopes. Special hidden-detail-removed projections are constructed which help visualize the structure of 4-polytopes. For both these hidden-detail- removed projections, and for the star-polyhedral shadows of star polytopes, methods are supplied to export into POV-Ray format.

*Mathematics > Geometry > Solid Geometry

Polytopes, 4-space, n-space
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RegularPolytopes.nb (442.4 KB) - Mathematica v.4 notebook