2 51 honeycomb
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| 251 honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform tessellation |
| Family | 2k1 polytope |
| Schläfli symbol | {3,3,35,1} |
| Coxeter symbol | 251 |
| Coxeter-Dynkin diagram | Template:CDD |
| 8-face types | 241 File:2 41 t0 E8.svg {37} File:8-simplex t0.svg |
| 7-face types | 231 File:Gosset 2 31 polytope.svg {36} File:7-simplex t0.svg |
| 6-face types | 221 File:E6 graph.svg {35} File:6-simplex t0.svg |
| 5-face types | 211 File:Cross graph 5.svg {34} File:5-simplex t0.svg |
| 4-face type | {33} File:4-simplex t0.svg |
| Cells | {32} File:3-simplex t0.svg |
| Faces | {3}File:2-simplex t0.svg |
| Vertex figure | 151 File:8-demicube.svg |
| Edge figure | 051 File:7-simplex t1.svg |
| Coxeter group | , [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, Template:Isbn (Chapter 3: Wythoff's Construction for Uniform Polytopes)
- Coxeter Regular Polytopes (1963), Macmillan Company
- Regular Polytopes, Third edition, (1973), Dover edition, Template: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, wiley.com, Template:Isbn
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]