Stericated 24-cell honeycomb
Stericated 24-cell honeycomb Stericated 16-cell honeycomb | |
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(No image) | |
Type | Uniform 4-honeycomb |
Schläfli symbol | t04{3,4,3,3} |
Coxeter-Dynkin diagrams | |
4-face type | {3,4,3} {3,3,4} {3,4}x{} {3,3}x{} {3}x{3} |
Cell type | {3,4} {3,3} {3}x{} |
Face type | {3}, {4} |
Vertex figure | |
Coxeter groups | , [3,4,3,3] |
Properties | Vertex transitive |
In four-dimensional Euclidean geometry, the stericated 24-cell honeycomb (or stericated 16-cell honeycomb) is a uniform space-filling honeycomb. It can be seen as a sterication of the regular 24-cell honeycomb, containing 24-cell, 16-cell, octahedral prism, tetrahedral prism, and 3-3 duoprism cells.
Alternate names
- Stericated icositetrachoric/hexadecaachoric tetracomb/honeycomb
- Small cellated demitesseractic tetracomb (scicot)
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 121 (Wrongly named runcinated icositetrachoric honeycomb)
- Klitzing, Richard. "4D Euclidean tesselations". x3o3o4o3x - scicot - O121
Fundamental convex regular and uniform honeycombs in dimensions 3–10 (or 2-9) | |||||
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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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