Английская Википедия:1 52 honeycomb
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| 152 honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform tessellation |
| Family | 1k2 polytope |
| Schläfli symbol | {3,35,2} |
| Coxeter symbol | 152 |
| Coxeter-Dynkin diagram | Шаблон:CDD |
| 8-face types | 142Файл:Gosset 1 42 polytope petrie.svg 151Файл:Demiocteract ortho petrie.svg |
| 7-face types | 132Файл:Gosset 1 32 petrie.svg 141Файл:Demihepteract ortho petrie.svg |
| 6-face types | 122Файл:Gosset 1 22 polytope.svg {31,3,1}Файл:Demihexeract ortho petrie.svg {35}Файл:6-simplex t0.svg |
| 5-face types | 121Файл:Demipenteract graph ortho.svg {34}Файл:5-simplex t0.svg |
| 4-face type | 111Файл:Cross graph 4.svg {33}Файл:4-simplex t0.svg |
| Cells | {32}Файл:3-simplex t0.svg |
| Faces | {3}Файл:2-simplex t0.svg |
| Vertex figure | birectified 8-simplex: t2{37} Файл:Birectified 8-simplex.png |
| Coxeter group | <math>{\tilde{E}}_8</math>, [35,2,1] |
In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 142 and 151 facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1k2 polytope 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 end of the 2-length branch leaves the 8-demicube, 151.
Removing the node on the end of the 5-length branch leaves the 142.
The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 052.
Related polytopes and honeycombs
See also
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] GoogleBook
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
