Cantitruncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the cantitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a cantitruncation of the regular 24-cell honeycomb, containing truncated tesseract, cantitruncated 24-cell, and tetrahedral prism cells.
Cantitruncated 24-cell honeycomb | |
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(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | tr{3,4,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-face type | t{4,3,3} tr{3,4,3} {3,3}×{} |
Cell type | |
Face type | |
Vertex figure | |
Coxeter groups | , [3,4,3,3] |
Properties | Vertex transitive |
Alternate names
- Cantelltaed icositetrachoric tetracomb/honeycomb
- Great rhombated icositetrachoric tetracomb (gricot)
- Great 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.
F4 honeycombs | |||
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Extended symmetry | Extended diagram | Order | Honeycombs |
[3,3,4,3] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ×1 | |
[3,4,3,3] | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ×1 |
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[(3,3)[3,3,4,3*]] =[(3,3)[31,1,1,1]] =[3,4,3,3] |
![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ×4 |
See also
Regular and uniform honeycombs in 4-space:
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 114
- Klitzing, Richard. "4D Euclidean tesselations". o3o3x4x3x - gricot - O114
Space | Family | / / | ||||
---|---|---|---|---|---|---|
E2 | Uniform tiling | {3[3]} | δ3 | hδ3 | qδ3 | Hexagonal |
E3 | Uniform convex honeycomb | {3[4]} | δ4 | hδ4 | qδ4 | |
E4 | Uniform 4-honeycomb | {3[5]} | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
E5 | Uniform 5-honeycomb | {3[6]} | δ6 | hδ6 | qδ6 | |
E6 | Uniform 6-honeycomb | {3[7]} | δ7 | hδ7 | qδ7 | 222 |
E7 | Uniform 7-honeycomb | {3[8]} | δ8 | hδ8 | qδ8 | 133 • 331 |
E8 | Uniform 8-honeycomb | {3[9]} | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
E9 | Uniform 9-honeycomb | {3[10]} | δ10 | hδ10 | qδ10 | |
E10 | Uniform 10-honeycomb | {3[11]} | δ11 | hδ11 | qδ11 | |
En-1 | Uniform (n-1)-honeycomb | {3[n]} | δn | hδn | qδn | 1k2 • 2k1 • k21 |
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