# Polytope Movie Page (Four Dimensions)

Schlegal diagram of a regular 4-dimensional polytope 24-cell. It has 24 facets each of which is a regular octahedron. In the schlegal diagram, we see all facets except one through a fixed tranparent facet. Thus we are seeing 23 octahedra packed in the (outer, light blue) octahedron. The furthest facet from the fixed facet is red. Do you see them all? They are distorted by a projective transformation from a 4-dim to a 3-dim space. The polytope is selfdual.

Schlegal diagram of a regular 4-dimensional polytope 120-cell. It has 120 facets each of which is a regular dodecahedron. In the schlegal diagram, we see all facets (except one) through a fixed facet. Thus we are seeing 119 dodecahedra packed in the (outer, light blue) dodecahedron. The middle one is colored red. The dual polytope is called 600-cell whose (600) facets are regular icosahedra.

The movies above have been created by the polyhedral computation code cdd+, Mathematica and Oliver Knill's package GMT (GifMovieTool). cdd/cdd+ packages contain vertex files of the polytopes above.

This page is written by Komei Fukuda (ETH Zurich, Switzerland) homepage, e-mail.
Last updated: September 16, 1998