24cell
Contents
EnglishEdit
EtymologyEdit
PronunciationEdit
 IPA^{(key)}: /twɛntiˈfoʊɹˌsɛl/
NounEdit
24cell (plural 24cells)
 (geometry) A fourdimensional polytope whose twentyfour bounding facets are octahedra and which has no threedimensional analogue.
 1995, Harold Scott Macdonald Coxeter, Paper Three: Two Aspects of the Regular 24Cell in Four Dimensions, F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Iviċ Weiss (editors), Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 25,
 The octagonal projection of the regular 24cell (3,4,3} reveals that the 24 vertices of this 4dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4cube γ_{4} = {4,3,3} and the 8 vertices of its dual, the 16cell β_{4} = {3,3,4}. This view of the 24cell is less wellknown than the dodecagonal projection, in which the β_{4} appears as two squares of different sizes joined by 8 equilateral triangles.
 2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445,
 One more example of a four dimensional tessellation is given using the 24cell, see Fig 2.
 2002, Gabor Toth, Glimpses of Algebra and Geometry, 2nd edition, page 385,
 The regular polytope with Schläfli symbol {3,4,3}, the socalled 24cell, can be obtained from the 16cell as follows. The vertices of the 24cell are the midpoints of the 24 edges of the 16cell.
 1995, Harold Scott Macdonald Coxeter, Paper Three: Two Aspects of the Regular 24Cell in Four Dimensions, F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Iviċ Weiss (editors), Kaleidoscopes: Selected Writings of H.S.M. Coxeter, page 25,
SynonymsEdit
 (4dimensional polytope with 24 octahedral facets): hyperdiamond, icositetrachoron, octacube, octaplex, polyoctahedron,
TranslationsEdit
fourdimensional polytope
