5-cell

English

A Schlegel diagram of a 5-cell

Etymology

From 5 +‎ cell.

Pronunciation

• IPA^(key): /ˈfaɪvˌsɛl/

Noun

5-cell (plural 5-cells)

1. (geometry) A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra.
   • 1896, American Journal of Mathematics, page 181:

     In every vertex of the 5-cell, 8-cell and 120-cell there are 4 concurring edges; in every vertex of the 24-cell, 8 edges.

   • 1988, Unnamed translator, L. A. Sidorov, Confuguration, article in Michiel Hazewinkel (editor) Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’, Volume 2: C, page 309,

     For example, a 5-cell is bounded by five three-dimensional tetrahedra, an 8-cell by eight cubes, etc., the 5-cell and the 24-cell being duals of each other (the points correspond to spaces and lines to planes).

   • 2007, Steven R. Lay, Convex Sets and Their Applications‎^[1], page 230:

     If we call a regular polytope with m facets an m-cell, then in E⁴ we have the 5-cell with tetrahedral facets (the simplex), the 8-cell with cubic facets (the hypercube), the 16-cell with tetrahedral facets (the regular cross-polytope), the 24-cell with octahedral facets, the 120-cell with dodecahedral facets, and the 600-cell with tetrahedral facets.

   • 2008, Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought‎^[2], page 16:

     Later in the same document, President Hall listed all of the university's four-dimensional models: four Brill models—the 5-cell, 8-cell, 16-cell, and 24-cell—along with seven spun glass models by T. P. Hall that "illustrated rotations."

Synonyms

• (4-dimensional polytope analogous to a tetrahedron): 4-simplex, pentachoron, pentahedroid, pentatope, tetrahedral pyramid

Translations

four-dimensional polytope analogous to a tetrahedron

• Esperanto: kvinĉelo
• Italian: 5-cella f, ipertetraedro m, pentacoro m
• Japanese: 正五胞体 (せいごほうたい, seigohōtai)