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"Developer Project Information" Russell Towle

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  • Subject: [mg20675] "Developer Project Information" Russell Towle
  • From: Russell Towle <rustybel at>
  • Date: Sun, 7 Nov 1999 02:10:09 -0500
  • Sender: owner-wri-mathgroup at

Title: Regular Polytopes
Author: Russell Towle
Format: Mathematica 4.0 notebook

"Polytope" is the general term for the sequence point, segment, polygon,
polyhedron. Of all the infinitude of polytopes which exist in n-dimensional
Euclidean spaces we may select those with the most symmetry. This somewhat
difficult subject is set forth in H.S.M. Coxeter's modern classic, "Regular
Polytopes" (Dover, 1973). It seems to me that what is needed, to bring
these wondrous and cheerful denizens of higher space down to earth, is
graphics, and whenever possible, animation.

In my Mathematica notebook, the sixteen regular polytopes in four
dimensions are constructed, along with another twelve polytopes of lesser
symmetry. Plane and solid projections are formed, as are solid sections.
Hidden-detail-removed projections of the convex 4-polytopes into a 3-space
are also constructed. By this means one obtains a larger polyhedron (the
orthogonal solid shadow) made of smaller polyhedra fitting together

The notebook is large and demands a degree of active participation upon the
part of the user. It is available at

Russell Towle
Box 141
Dutch Flat, CA 95714
(530) 389-2872

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