| Stericantic tesseractic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Schläfli symbol | h2,4{4,3,3,4} |
| Coxeter-Dynkin diagram | = |
| 4-face type | rr{4,3,3}t0,1,3{3,3,4}t{3,3,4}{3,3}×{} |
| Cell type | rr{4,3}{3,4}{4,3}t{3,3}t{3}×{}{3}×{} |
| Face type | {6}{4}{3} |
| Vertex figure | |
| Coxeter group | B ~ 4 {\displaystyle {\tilde {B}}_{4}} = [4,3,31,1] |
| Dual | ? |
| Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the stericantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
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Alternate names
- Prismatotruncated demitesseractic tetracomb (pithatit)
- Small prismatodemitesseractic tetracomb
Related honeycombs
The [4,3,31,1], , Coxeter group generates 31 permutations of uniform tessellations, 23 with distinct symmetry and 4 with distinct geometry. There are two alternated forms: the alternations (19) and (24) have the same geometry as the 16-cell honeycomb and snub 24-cell honeycomb respectively.
| B4 honeycombs | ||||
|---|---|---|---|---|
| Extendedsymmetry | Extendeddiagram | Order | Honeycombs | |
| [4,3,31,1]: | ×1 | |||
| <[4,3,31,1]>:↔[4,3,3,4] | ↔ | ×2 | ||
| [3[1+,4,3,31,1]]↔ [3[3,31,1,1]]↔ [3,3,4,3] | ↔ ↔ | ×3 | ||
| [(3,3)[1+,4,3,31,1]]↔ [(3,3)[31,1,1,1]]↔ [3,4,3,3] | ↔ ↔ | ×12 | ||
See also
Regular and uniform honeycombs in 4-space:
- Tesseractic honeycomb
- 16-cell honeycomb
- 24-cell honeycomb
- Rectified 24-cell honeycomb
- Truncated 24-cell honeycomb
- Snub 24-cell honeycomb
- 5-cell honeycomb
- Truncated 5-cell honeycomb
- Omnitruncated 5-cell honeycomb
Notes
- 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". x3x3o *b3o4x - pithatit - O109
| ||||||
|---|---|---|---|---|---|---|
| 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 |