Quarter 7-cubic honeycomb

quarter 7-cubic honeycomb
(No image)
TypeUniform 7-honeycomb
FamilyQuarter hypercubic honeycomb
Schläfli symbolq{4,3,3,3,3,3,4}
Coxeter diagram =
6-face typeh{4,35},
h5{4,35},
{31,1,1}×{3,3} duoprism
Vertex figure
Coxeter group{\tilde{D}}_7×2 = [[3<sup>1,1</sup>,3,3,3,3<sup>1,1</sup>]]
Dual
Propertiesvertex-transitive

In seven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 7-demicubic honeycomb, and a quarter of the vertices of a 7-cube honeycomb.[1] Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms.

Related honeycombs

This honeycomb is one of 77 uniform honycombs constructed by the {\tilde{D}}_7 Coxeter group, all but 10 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 77 permutations are listed with its highest extended symmetry, and related {\tilde{B}}_7 and {\tilde{C}}_7 constructions:

See also

Regular and uniform honeycombs in 7-space:

Notes

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

References

Fundamental convex regular and uniform honeycombs in dimensions 2–10
Family {\tilde{A}}_{n-1} {\tilde{C}}_{n-1} {\tilde{B}}_{n-1} {\tilde{D}}_{n-1} {\tilde{G}}_2 / {\tilde{F}}_4 / {\tilde{E}}_{n-1}
Uniform tiling {3[3]} δ3 hδ3 qδ3 Hexagonal
Uniform convex honeycomb {3[4]} δ4 hδ4 qδ4
Uniform 5-honeycomb {3[5]} δ5 hδ5 qδ5 24-cell honeycomb
Uniform 6-honeycomb {3[6]} δ6 hδ6 qδ6
Uniform 7-honeycomb {3[7]} δ7 hδ7 qδ7 222
Uniform 8-honeycomb {3[8]} δ8 hδ8 qδ8 133 • 331
Uniform 9-honeycomb {3[9]} δ9 hδ9 qδ9 152 • 251 • 521
Uniform n-honeycomb {3[n]} δn hδn qδn 1k2 • 2k1 • k21
This article is issued from Wikipedia - version of the Monday, September 21, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.