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Quarter 8-cubic honeycomb

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quarter 8-cubic honeycomb
(No image)
TypeUniform 8-honeycomb
FamilyQuarter hypercubic honeycomb
Schläfli symbolq{4,3,3,3,3,3,3,4}
Coxeter diagram =
7-face typeh{4,36},
h6{4,36},
{3,3}×{32,1,1} duoprism
{31,1,1}×{31,1,1} duoprism
Vertex figure
Coxeter group D ~ 8 {\displaystyle {\tilde {D}}_{8}} {\displaystyle {\tilde {D}}_{8}}×2 = [[31,1,3,3,3,3,31,1]]
Dual
Propertiesvertex-transitive

In seven-dimensional Euclidean geometry, the quarter 8-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 8-demicubic honeycomb, and a quarter of the vertices of a 8-cube honeycomb.[1] Its facets are 8-demicubes h{4,36}, pentic 8-cubes h6{4,36}, {3,3}×{32,1,1} and {31,1,1}×{31,1,1} duoprisms.

See also

Regular and uniform honeycombs in 8-space:

Notes

  1. Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318

References

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