Английская Википедия:Bitruncated 16-cell honeycomb
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| Bitruncated 16-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Schläfli symbol | t1,2{3,3,4,3} h2,3{4,3,3,4} 2t{3,31,1,1} |
| Coxeter-Dynkin diagram | Шаблон:CDD Шаблон:CDD = Шаблон:CDD Шаблон:CDD = Шаблон:CDD |
| 4-face type | Truncated 24-cell Файл:Schlegel half-solid truncated 24-cell.png Bitruncated tesseract Файл:Schlegel half-solid bitruncated 16-cell.png |
| Cell type | Cube Файл:Hexahedron.png Truncated octahedron Файл:Truncated octahedron.png Truncated tetrahedron Файл:Truncated tetrahedron.png |
| Face type | {3}, {4}, {6} |
| Vertex figure | |
| Coxeter group | <math>{\tilde{F}}_4</math> = [3,3,4,3] <math>{\tilde{B}}_4</math> = [4,3,31,1] <math>{\tilde{D}}_4</math> = [31,1,1,1] |
| Dual | ? |
| Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Symmetry constructions
There are 3 different symmetry constructions, all with 3-3 duopyramid vertex figures. The <math>{\tilde{B}}_4</math> symmetry doubles on <math>{\tilde{D}}_4</math> in three possible ways, while <math>{\tilde{F}}_4</math> contains the highest symmetry.
| Affine Coxeter group | <math>{\tilde{F}}_4</math> [3,3,4,3] |
<math>{\tilde{B}}_4</math> [4,3,31,1] |
<math>{\tilde{D}}_4</math> [31,1,1,1] |
|---|---|---|---|
| Coxeter diagram | Шаблон:CDD | Шаблон:CDD | Шаблон:CDD |
| 4-faces | Шаблон:CDD Шаблон:CDD |
Шаблон:CDD Шаблон:CDD Шаблон:CDD |
Шаблон:CDD Шаблон:CDD |
See also
Regular and uniform honeycombs in 4-space:
- Tesseractic honeycomb
- 16-cell honeycomb
- 24-cell honeycomb
- Rectified 24-cell honeycomb
- Truncated 24-cell honeycomb
- Snub 24-cell honeycomb
- 5-cell honeycomb
- Truncated 5-cell honeycomb
- Omnitruncated 5-cell honeycomb
Notes
References
- 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]
- George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
- Шаблон:KlitzingPolytopes x3x3x *b3x *b3o, x3x3o *b3x4o, o3x3x4o3o - bithit - O107
