Dictionary

5-cell en · NOUN

Pronunciation

• /ˈfaɪvˌsɛl/

Etymology

From 5 + cell.

Meanings

1. A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra.
   • 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. 1896, American Journal of Mathematics, page 181:
   • 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. 2007, Steven R. Lay, Convex Sets and Their Applications, page 230:
   • 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." 2008, Tony Robbin, Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought, page 16:
   • 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). 1988, L. A. Sidorov, “Confuguration”, in Unnamed, transl., edited by Michiel Hazewinkel, Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’, Volume 2: C, page 309:

Forms

Synonyms

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

Translations (7)

pl pięciościan czterowymiarowy (four-dimensional polytope analogous to a tetrahedron) · it ipertetraedro (four-dimensional polytope analogous to a tetrahedron) · ko 정오포체 (four-dimensional polytope analogous to a tetrahedron) · it pentacoro (four-dimensional polytope analogous to a tetrahedron) · it 5-cella (four-dimensional polytope analogous to a tetrahedron) · eo kvinĉelo (four-dimensional polytope analogous to a tetrahedron) · ja 正五胞体 (four-dimensional polytope analogous to a tetrahedron)