600-cell

English

A vertex-centred Schlegel diagram of a 600-cell

Noun

600-cell (plural 600-cells)

1. (geometry) A four-dimensional polytope, analogous to an icosahedron, whose 600 bounding facets are tetrahedra.
   • 1995, J. Bokowski, On the Construction of Equifacetted 3-Spheres, Neil L. White, Invariant Methods in Discrete and Computational Geometry: Proceedings of the Curaçao Conference, page 303,

     P. McMullen has pointed out to the author that he has constructed an interesting equifacetted 3-sphere in his Ph.D.Thesis by starting with the 600-cell.

   • 2005, Lawrence B. Crowell, Quantum Fluctuations of Spacetime, volume 25, World Scientific Series in Contemporary Chemical Physics, page 329:

     The dual to the 120-cell is the 600-cell. The 600-cell is a 4-dimensional convex regular polytope with 600 facets. Its Schläfli symbol of the^[sic] 600-cell is {3, 3, 5}. It is a 4-dimensional analogue of the icosahedron, constructed by the golden ratio on the edges of an octohedron.

   • 2012, John Barnes, Gems of Geometry, 2nd edition, page 79:

     The other two figures are the 120-cell and 600-cell which form a dual pair as is clear from their Schläfli symbols being the reverse of each other.

Synonyms

• (4-dimensional polytope): hexacosichoron, hexacosidedroid

Hypernyms

• (4-dimensional polytope): tetraplex, polytetrahedron

Derived terms

• grand 600-cell

Translations

four-dimensional polytope

• Esperanto: sescentĉelo
• Italian: 600-cella f, tetraplesso m, esacosicoro m
• Japanese: 正六百胞体 (せいろっぴゃくほうたい, seiroppyakuhōtai)
• Spanish: hexacosicoron m