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Quarter 7-cubic honeycomb

Tessellation in Euclidean geometry From Wikipedia, the free encyclopedia

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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.

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×2 = [[31,1,3,3,3,31,1]]
Dual
Propertiesvertex-transitive
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This honeycomb is one of 77 uniform honeycombs constructed by the 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 and constructions:

More information D7 honeycombs, Extendedsymmetry ...
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See also

Regular and uniform honeycombs in 7-space:

Notes

References

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