120-cell

Definitions

1. 1

   A four-dimensional polytope, analogous to a dodecahedron, whose 120 bounding facets are…

   A four-dimensional polytope, analogous to a dodecahedron, whose 120 bounding facets are dodecahedra.

   • The triacontagonal projection of the 120-cell was first drawn by W. A. Wythoff, but not in reproducible form.
   • In dimension four there are ten star polytopes which together with the 120-cell and 600-cell form the family of pentagonal polytopes (those regular 4-polytopes possessing axes of fivefold symmetry); all twelve have the same symmetry group.
   • In 1985, M. Davis [3] gave the first explicit geometric construction of a closed hyperbolic 4-manifold by gluing together the opposite sides of a regular hyperbolic 120-cell P with dihedral angle 72°.

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