Steriruncicantic tesseractic honeycomb

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In four-dimensional Euclidean geometry, the steriruncicantic tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.

Steriruncicantic tesseractic honeycomb
(No image)
TypeUniform honeycomb
Schläfli symbolh2,3,4{4,3,3,4}
Coxeter-Dynkin diagram =
4-face typet0123{4,3,3}
tr{4,3,3}
2t{4,3,3}
t{3,3}×{}
Cell typetr{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?
Propertiesvertex-transitive

Alternate names

  • great prismated demitesseractic tetracomb (giphatit)
  • great diprismatodemitesseractic tetracomb

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.

More information B4 honeycombs, Extendedsymmetry ...
B4 honeycombs
Extended
symmetry
Extended
diagram
Order Honeycombs
[4,3,31,1]: ×1

5, 6, 7, 8

<[4,3,31,1]>:
↔[4,3,3,4]

×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]


×3

1, 2, 3, 4

[(3,3)[1+,4,3,31,1]]
↔ [(3,3)[31,1,1,1]]
↔ [3,4,3,3]


×12

20, 21, 22, 23

Close

See also

Regular and uniform honeycombs in 4-space:

Notes

References

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