Quarter 7-cubic honeycomb

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quarter 7-cubic honeycomb
(No image)
Type Uniform 7-honeycomb
Family Quarter hypercubic honeycomb
Schläfli symbol q{4,3,3,3,3,3,4}
Coxeter diagram CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes 10lu.png = CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node h1.png
6-face type h{4,35}, 7-demicube t0 D7.svg
h5{4,35}, 7-demicube t05 D7.svg
{31,1,1}×{3,3} duoprism
Vertex figure
Coxeter group ×2 = [[31,1,3,3,3,31,1]]
Dual
Properties vertex-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[edit]

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:

See also[edit]

Regular and uniform honeycombs in 7-space:

Notes[edit]

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

References[edit]

  • 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 [1]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 [2]
  • Klitzing, Richard. "7D Euclidean tesselations#7D". 
Fundamental convex regular and uniform honeycombs in dimensions 2-9
Space Family / /
E2 Uniform tiling {3[3]} δ3 3 3 Hexagonal
E3 Uniform convex honeycomb {3[4]} δ4 4 4
E4 Uniform 4-honeycomb {3[5]} δ5 5 5 24-cell honeycomb
E5 Uniform 5-honeycomb {3[6]} δ6 6 6
E6 Uniform 6-honeycomb {3[7]} δ7 7 7 222
E7 Uniform 7-honeycomb {3[8]} δ8 8 8 133331
E8 Uniform 8-honeycomb {3[9]} δ9 9 9 152251521
E9 Uniform 9-honeycomb {3[10]} δ10 10 10
En-1 Uniform (n-1)-honeycomb {3[n]} δn n n 1k22k1k21