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Steriruncicantic tesseractic honeycomb

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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}
×ばつ{}
Cell type tr{4,3}
t{3,4}
t{3,3}
×ばつ{}
×ばつ{}
×ばつ{}
Face type {8}
{6}
{4}
Vertex figure
Coxeter group B ~ 4 {\displaystyle {\tilde {B}}_{4}} {\displaystyle {\tilde {B}}_{4}} = [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

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  • great prismated demitesseractic tetracomb (giphatit)
  • great diprismatodemitesseractic tetracomb
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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]: ×ばつ1

5 , 6 , 7 , 8

<[4,3,31,1]>:
↔[4,3,3,4]
↔ 		×ばつ2

9 , 10 , 11 , 12 , 13 , 14 ,

(10) , 15 , 16 , (13) , 17 , 18 , 19

[3[1+,4,3,31,1]]
↔ [3[3,31,1,1]]
↔ [3,3,4,3]
↔
↔ 		×ばつ3

1 , 2 , 3 , 4

[(3,3)[1+,4,3,31,1]]
↔ [(3,3)[31,1,1,1]]
↔ [3,4,3,3]
↔
↔ 		×ばつ12

20 , 21 , 22 , 23

See also

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Regular and uniform honeycombs in 4-space:

Notes

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References

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  • 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
Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space Family A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} {\displaystyle {\tilde {A}}_{n-1}} C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} {\displaystyle {\tilde {C}}_{n-1}} B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} {\displaystyle {\tilde {B}}_{n-1}} D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} {\displaystyle {\tilde {D}}_{n-1}} G ~ 2 {\displaystyle {\tilde {G}}_{2}} {\displaystyle {\tilde {G}}_{2}} / F ~ 4 {\displaystyle {\tilde {F}}_{4}} {\displaystyle {\tilde {F}}_{4}} / E ~ n − 1 {\displaystyle {\tilde {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

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