Quarter 8-cubic honeycomb

quarter 8-cubic honeycomb
(No image)
Type	Uniform 8-honeycomb
Family	Quarter hypercubic honeycomb
Schläfli symbol	q{4,3,3,3,3,3,3,4}
Coxeter diagram	=
7-face type	h{4,36}, h6{4,36}, {3,3}×{32,1,1} duoprism {31,1,1}×{31,1,1} duoprism
Vertex figure
Coxeter group	${\displaystyle {\tilde {D}}_{8}}$×2 = [[31,1,3,3,3,3,31,1]]
Dual
Properties	vertex-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}×{3^2,1,1} and {3^1,1,1}×{3^1,1,1} duoprisms.

See also

Regular and uniform honeycombs in 8-space:

• 8-cube honeycomb
• 8-demicube honeycomb
• 8-simplex honeycomb
• Truncated 8-simplex honeycomb
• Omnitruncated 8-simplex honeycomb

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 Archived 2016-07-11 at the Wayback Machine
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
• Klitzing, Richard. "7D Euclidean tesselations#7D".

v t e Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space	Family	${\displaystyle {\tilde {A}}_{n-1}}$	${\displaystyle {\tilde {C}}_{n-1}}$	${\displaystyle {\tilde {B}}_{n-1}}$	${\displaystyle {\tilde {D}}_{n-1}}$	${\displaystyle {\tilde {G}}_{2}}$ / ${\displaystyle {\tilde {F}}_{4}}$ / ${\displaystyle {\tilde {E}}_{n-1}}$
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