# Polytope Movie Page (Four Dimensions)

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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