| Stericantitruncated tesseractic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Schläfli symbol | t0,1,2,4{4,3,3,4} |
| Coxeter-Dynkin diagrams | |
| 4-face type | runcitruncated 16-cell cantitruncated tesseract rhombicuboctahedral prism truncated cuboctahedral prism 4-8 duoprism |
| Cell type | Truncated cuboctahedron Rhombicuboctahedron Truncated tetrahedron Octagonal prism Hexagonal prism Cube Triangular prism |
| Face type | {3}, {4}, {6}, {8} |
| Vertex figure | irr. square pyramid pyramid |
| Coxeter groups | C ~ 4 {\displaystyle {\tilde {C}}_{4}} , [4,3,3,4] |
| Properties | Vertex transitive |
In four-dimensional Euclidean geometry, the stericantitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It is composed of runcitruncated 16-cell, cantitruncated tesseract, rhombicuboctahedral prism, truncated cuboctahedral prism, and 4-8 duoprism facets, arranged around an irregular 5-cell vertex figure.
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 | |||
|---|---|---|---|
| Extendedsymmetry | Extendeddiagram | 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
- 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 [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)
- Klitzing, Richard. "4D Euclidean tesselations". x4x3x3o4x - gicartit - O101
| ||||||
|---|---|---|---|---|---|---|
| Space | Family | A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} | C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} | B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} | D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} | G ~ 2 {\displaystyle {\tilde {G}}_{2}} / F ~ 4 {\displaystyle {\tilde {F}}_{4}} / E ~ n − 1 {\displaystyle {\tilde {E}}_{n-1}} |
| E2 | Uniform tiling | 0[3] | δ3 | hδ3 | qδ3 | Hexagonal |
| E3 | Uniform convex honeycomb | 0[4] | δ4 | hδ4 | qδ4 | |
| E4 | Uniform 4-honeycomb | 0[5] | δ5 | hδ5 | qδ5 | 24-cell honeycomb |
| E5 | Uniform 5-honeycomb | 0[6] | δ6 | hδ6 | qδ6 | |
| E6 | Uniform 6-honeycomb | 0[7] | δ7 | hδ7 | qδ7 | 222 |
| E7 | Uniform 7-honeycomb | 0[8] | δ8 | hδ8 | qδ8 | 133 • 331 |
| E8 | Uniform 8-honeycomb | 0[9] | δ9 | hδ9 | qδ9 | 152 • 251 • 521 |
| E9 | Uniform 9-honeycomb | 0[10] | δ10 | hδ10 | qδ10 | |
| E10 | Uniform 10-honeycomb | 0[11] | δ11 | hδ11 | qδ11 | |
| En−1 | Uniform (n−1)-honeycomb | 0[n] | δn | hδn | qδn | 1k2 • 2k1 • k21 |