16-cell

English

A 16-cell (Schlegel diagram)

Etymology

From 16 +‎ cell.

Pronunciation

• IPA^(key): /sɪksˈtiːnˌsɛl/

• Audio (US):

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Noun

16-cell (plural 16-cells)

1. (geometry) A four-dimensional polytope, analogous to an octahedron, whose sixteen bounding facets are tetrahedra.
   • 1995, Harold Scott Macdonald Coxeter, “Paper Three: Two Aspects Of The Regular 24-Cell In Four Dimensions”, in F. Arthur Sherk, editor, Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 32:

     The remaining 8, as before, are the vertices of the complementary 16-cell (see Figure 9). In Figure 7, these 8 points have been blackened, but not joined, because the 16-cell has longer edges; diameters of octahedral facets of the 24-cell.

   • 2002, Gabor Toth, Glimpses of Algebra and Geometry, 2nd edition, page 385:

     This polytope has 16 tetrahedral cells, and for this reason it is called the 16-cell. […] The 16-cell has 24 edges that are the diagonals of the 24 square faces of the hypercube. (Since we are selecting alternate vertices of the hypercube, we only get one diagonal for each square face.)

   • 2012, John Barnes, Gems of Geometry, 2nd edition, page 76:

     We will now consider the dual 16-cell. In some ways the 16-cell is a bit easier because it has fewer vertices and edges. But on the other hand the hypercube is perhaps easier to understand intuitively because we can readily (perhaps) see the various cubes of which it is composed.

Synonyms

• (4-dimensional polytope analogous to an octahedron): 4-orthoplex, 4-demicube, 4-hemicube, demihypercube, demitesseract, hexadecachoron, hexadecahedroid

Translations

four-dimensional object

• Esperanto: deksesĉelo
• Italian: 16-cella f, 4-ortoplesso m, ipertetraedro m, esadecacoro m
• Japanese: 正十六胞体 (せいじゅうろくほうたい, seijūrokuhōtai)
• Korean: 정십육포체(正十六胞體) (jeongsibyukpoche)
• Russian: шестнадцатиячейник (ru) (šestnadcatijačejnik)