Steriruncicantic tesseractic honeycomb
Appearance
Steriruncicantic tesseractic honeycomb | |
---|---|
(No image) | |
Type | Uniform honeycomb |
Schläfli symbol | h2,3,4{4,3,3,4} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4-face type | t0123{4,3,3} ![]() tr{4,3,3} ![]() 2t{4,3,3} ![]() t{3,3}×{} ![]() |
Cell type | tr{4,3} ![]() t{3,4} ![]() t{3,3} ![]() t{4}×{} ![]() t{3}×{} ![]() {3}×{} ![]() |
Face type | {8} {6} {4} |
Vertex figure | |
Coxeter group | = [4,3,31,1] |
Dual | ? |
Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the steriruncicantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Alternate names
[edit]- great prismated demitesseractic tetracomb (giphatit)
- great diprismatodemitesseractic tetracomb
Related honeycombs
[edit]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 | ||||
---|---|---|---|---|
Extended symmetry |
Extended diagram |
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
[edit]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
[edit]References
[edit]- 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 *b3x4x - giphatit - O111
Space | Family | / / | ||||
---|---|---|---|---|---|---|
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 |