Quarter 5-cubic honeycomb

In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb.[1] Its facets are 5-demicubes and runcinated 5-demicubes.

quarter 5-cubic honeycomb
(No image)
TypeUniform 5-honeycomb
FamilyQuarter hypercubic honeycomb
Schläfli symbolq{4,3,3,3,4}
Coxeter-Dynkin diagram =
5-face typeh{4,33},
h4{4,33},
Vertex figure
Rectified 5-cell antiprism
or Stretched birectified 5-simplex
Coxeter group×2 = [[3<sup>1,1</sup>,3,3<sup>1,1</sup>]]
Dual
Propertiesvertex-transitive

This honeycomb is one of 20 uniform honeycombs constructed by the Coxeter group, all but 3 repeated in other families by extended symmetry, seen in the graph symmetry of rings in the Coxeter–Dynkin diagrams. The 20 permutations are listed with its highest extended symmetry relation:

See also

Regular and uniform honeycombs in 5-space:

Notes

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

References

  • 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
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
  • Klitzing, Richard. "5D Euclidean tesselations#5D". x3o3o x3o3o *b3*e - spaquinoh
Space Family / /
E2 Uniform tiling {3[3]} δ3 hδ3 qδ3 Hexagonal
E3 Uniform convex honeycomb {3[4]} δ4 hδ4 qδ4
E4 Uniform 4-honeycomb {3[5]} δ5 hδ5 qδ5 24-cell honeycomb
E5 Uniform 5-honeycomb {3[6]} δ6 hδ6 qδ6
E6 Uniform 6-honeycomb {3[7]} δ7 hδ7 qδ7 222
E7 Uniform 7-honeycomb {3[8]} δ8 hδ8 qδ8 133331
E8 Uniform 8-honeycomb {3[9]} δ9 hδ9 qδ9 152251521
E9 Uniform 9-honeycomb {3[10]} δ10 hδ10 qδ10
En-1 Uniform (n-1)-honeycomb {3[n]} δn hδn qδn 1k22k1k21
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