120-cell

English

A Schlegel diagram of a 120-cell

Noun

120-cell (plural 120-cells)

1. (geometry) A four-dimensional polytope, analogous to a dodecahedron, whose 120 bounding facets are dodecahedra.
   • 1964, Canadian Mathematical Bulletin, page 394:

     The triacontagonal projection of the 120-cell was first drawn by W. A. Wythoff, but not in reproducible form.

   • 1987, Jeffrey Hurst Butler, Hyperplane sections of regular star polytopes‎^[1], page 28:

     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.

   • 2006, John G. Radcliffe, “The Geometry of Hyperbolic Manifolds of Dimension a least 4”, in András Prékopa, Emil Molnár, editors, Non-Euclidean Geometries: János Bolyai Memorial Volume, page 270:

     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°.

Synonyms

• (four-dimensional polytope): dodecacontachoron, dodecaplex, hecatonicosachoron, hecatonicosahedroid, hyperdodecahedron, polydodecahedron

Derived terms

• Davis 120-cell (4-dimensional manifold in hyperbolic geometry constructed from a hyperbolic 120-cell),
• grand 120-cell
• grand stellated 120-cell
• great 120-cell
• great stellated 120-cell
• great grand 120-cell
• great grand stellated 120-cell
• small stellated 120-cell

Translations

four-dimensional polytope

• Esperanto: centdudekĉelo
• Italian: 120-celle m, iperdodecaedro m
• Japanese: 正百二十胞体 (せいひゃくにじゅうほうたい, seihyakunijūhōtai)