Английская Википедия:2 51 honeycomb
251 honeycomb | |
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(No image) | |
Type | Uniform tessellation |
Family | 2k1 polytope |
Schläfli symbol | {3,3,35,1} |
Coxeter symbol | 251 |
Coxeter-Dynkin diagram | Шаблон:CDD |
8-face types | 241Файл:Gosset 2 41 petrie.svg {37}Файл:8-simplex t0.svg |
7-face types | 231Файл:Gosset 2 31 polytope.svg {36}Файл:7-simplex t0.svg |
6-face types | 221Файл:E6 graph.svg {35}Файл:6-simplex t0.svg |
5-face types | 211Файл:Cross graph 5.svg {34}Файл:5-simplex t0.svg |
4-face type | {33}Файл:4-simplex t0.svg |
Cells | {32}Файл:3-simplex t0.svg |
Faces | {3}Файл:2-simplex t0.svg |
Edge figure | 051 Файл:6-simplex t1.svg |
Vertex figure | 151 Файл:8-demicube.svg |
Edge figure | 051 Файл:7-simplex t1.svg |
Coxeter group | <math>{\tilde{E}}_8</math>, [35,2,1] |
In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation. It is composed of 241 polytope and 8-simplex facets arranged in an 8-demicube vertex figure. It is the final figure in the 2k1 family.
Construction
It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space.
The facet information can be extracted from its Coxeter-Dynkin diagram.
Removing the node on the short branch leaves the 8-simplex.
Removing the node on the end of the 5-length branch leaves the 241.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the 8-demicube, 151.
The edge figure is the vertex figure of the vertex figure. This makes the rectified 7-simplex, 051.
Related polytopes and honeycombs
References
- Coxeter The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, Шаблон:ISBN (Chapter 3: Wythoff's Construction for Uniform Polytopes)
- Coxeter Regular Polytopes (1963), Macmillan Company
- Regular Polytopes, Third edition, (1973), Dover edition, Шаблон:ISBN (Chapter 5: The Kaleidoscope)
- 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, Шаблон:ISBN [1]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]