• Source: Truncated 24-cell honeycomb

In four-dimensional Euclidean geometry, the 24.3/info/truncated" target="_blank">truncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a truncation of the regular 24-cell honeycomb, containing tesseract and 24.3/info/truncated" target="_blank">truncated 24-cell cells.
It has a uniform alternation, called the snub 24-cell honeycomb. It is a snub from the







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4




{\displaystyle {\tilde {D}}_{4}}

construction. This 24.3/info/truncated" target="_blank">truncated 24-cell has Schläfli symbol t{31,1,1,1}, and its snub is represented as s{31,1,1,1}.




Alternate names


24.3/info/truncated" target="_blank">Truncated icositetrachoric tetracomb
24.3/info/truncated" target="_blank">Truncated icositetrachoric honeycomb
Cantitruncated 16-cell honeycomb
Bicantitruncated tesseractic honeycomb




Symmetry constructions


There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored 24.3/info/truncated" target="_blank">truncated 24-cell facets. In all cases, four 24.3/info/truncated" target="_blank">truncated 24-cells, and one tesseract meet at each vertex, but the vertex figures have different symmetry generators.




See also


Regular and uniform honeycombs in 4-space:

Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
24.3/info/truncated" target="_blank">Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb




References


Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 99
Klitzing, Richard. "4D Euclidean tesselations". o4x3x3x4o, x3x3x *b3x4o, x3x3x *b3x *b3x, o3o3o4x3x, x3x3x4o3o - ticot - O99

Kata Kunci Pencarian:

• Daftar bentuk matematika
• Truncated 24-cell honeycomb
• 24-cell honeycomb
• 5-cell honeycomb
• Truncated 16-cell honeycomb
• List of polygons, polyhedra and polytopes
• List of mathematical shapes
• 16-cell honeycomb
• Snub 24-cell honeycomb
• Cubic honeycomb
• Tetrahedral-octahedral honeycomb