Stericantellated tesseractic honeycomb
| Stericantellated tesseractic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Schläfli symbol | t0,2,4{4,3,3,4} |
| Coxeter-Dynkin diagrams |     |
| 4-face type | Tesseract  Cantellated tesseract  Rhombicuboctahedral prism  |
| Cell type | Rhombicuboctahedron  Cube  Octahedron  Triangular prism  |
| Face type | {3}, {4} |
| Vertex figure | Tetrahedral prismoid |
| Coxeter groups |  ×2, 4,3,3,4 |
| Properties | Vertex transitive |
In four-dimensional Euclidean geometry, the stericantellated tesseractic honeycomb is a uniform space-filling honeycomb.
Related honeycombs
The [4,3,3,4], , Coxeter group generates 31 permutations of uniform tessellations, 21 with distinct symmetry and 20 with distinct geometry. The expanded tesseractic honeycomb (also known as the stericated tesseractic honeycomb) is geometrically identical to the tesseractic honeycomb. Three of the symmetric honeycombs are shared in the [3,4,3,3] family. Two alternations (13) and (17), and the quarter tesseractic (2) are repeated in other families.
| C4 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Order | Honeycombs |
| [4,3,3,4]: | |
×1 | |
| [[4,3,3,4]] |      |
×2 | (1),  (2),  (13), 18 (6), 19, 20 |
| [(3,3)[1+,4,3,3,4,1+]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3] |
  ↔  ↔  |
×6 | |
See also
Regular and uniform honeycombs in 4-space:
- Tesseractic honeycomb
- 16-cell honeycomb
- 24-cell honeycomb
- Truncated 24-cell honeycomb
- Snub 24-cell honeycomb
- 5-cell honeycomb
- Truncated 5-cell honeycomb
- Omnitruncated 5-cell honeycomb
References
- Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
- 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
- (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)
- Richard Klitzing, 4D, Euclidean tesselations x4o3x3o4x - scartit - O98
| Fundamental convex regular and uniform honeycombs in dimensions 2–10 | |||||
|---|---|---|---|---|---|
| Family |  |
 |
 |
 |
 /  /  |
| Uniform tiling | {3[3]} | δ3 | hδ3 | qδ3 | Hexagonal |
| Uniform convex honeycomb | {3[4]} | δ4 | hδ4 | qδ4 | |
| Uniform 5-honeycomb | {3[5]} | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
| Uniform 6-honeycomb | {3[6]} | δ6 | hδ6 | qδ6 | |
| Uniform 7-honeycomb | {3[7]} | δ7 | hδ7 | qδ7 | 222 |
| Uniform 8-honeycomb | {3[8]} | δ8 | hδ8 | qδ8 | 133 • 331 |
| Uniform 9-honeycomb | {3[9]} | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
| Uniform n-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |
This article is issued from Wikipedia - version of the Monday, September 21, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.