Cantellated 24-cell honeycomb
| Cantellated 24-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform 4-honeycomb |
| Schläfli symbol | rr{3,4,3,3} s2{3,4,3,3} |
| Coxeter-Dynkin diagrams |      |
| 4-face type | rr{3,4,3}  r{3,4,3}  {3,3}×{}  |
| Cell type | rr{4,3} r{4,3} {3,3} {3}×{} |
| Face type | {3}, {4} |
| Vertex figure | |
| Coxeter groups | , [3,4,3,3] |
| Properties | Vertex transitive |
In four-dimensional Euclidean geometry, the cantellated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantellation of the regular 24-cell honeycomb, containing rectified tesseract, cantellated 24-cell, and tetrahedral prism cells.
Alternate names
- Cantellated icositetrachoric tetracomb/honeycomb
- Small rhombated demitesseractic tetracom (sricot)
- Small prismatodisicositetrachoric tetracomb
Related honeycombs
The [3,4,3,3], , Coxeter group generates 31 permutations of uniform tessellations, 28 are unique in this family and ten are shared in the [4,3,3,4] and [4,3,31,1] families. The alternation (13) is also repeated in other families.
See also
Regular and uniform honeycombs in 4-space:
- Tesseractic honeycomb
- 16-cell honeycomb
- 24-cell honeycomb
- Rectified 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) Model 112
- Klitzing, Richard. "4D Euclidean tesselations". o3o3x4o3x - sricot - O112
| Fundamental convex regular and uniform honeycombs in dimensions 3–10 (or 2-9) | |||||
|---|---|---|---|---|---|
| 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 10-honeycomb | {3[10]} | δ10 | hδ10 | qδ10 | |
| Uniform n-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |
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