152 honeycomb
| 152 honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform tessellation |
| Family | 1k2 polytope |
| Schläfli symbol | {3,35,2} |
| Coxeter symbol | 152 |
| Coxeter-Dynkin diagram | |
| 8-face types | 142 151 |
| 7-face types | 132 141 |
| 6-face types | 122 {31,3,1} {35} |
| 5-face types | 121 {34} |
| 4-face type | 111 {33} |
| Cells | {32} |
| Faces | {3} |
| Vertex figure | birectified 8-simplex: t2{37} |
| Coxeter group |  , [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 demiocteract, 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.
See also
References
- Coxeter The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN 978-0-486-40919-1 (Chapter 3: Wythoff's Construction for Uniform Polytopes)
- Coxeter Regular Polytopes (1963), Macmillian Company
- Regular Polytopes, Third edition, (1973), Dover edition, ISBN 0-486-61480-8 (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, ISBN 978-0-471-01003-6 [1] GoogleBook
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]