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}×{3^2,1,1} duoprism {3^1,1,1}×{3^1,1,1} duoprism
Vertex figure
Coxeter group	${{\tilde {D}}}_{8}$ ×2 = [[3<sup>1,1</sup>,3,3,3,3,3<sup>1,1</sup>]]
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.

Notes

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. "7D Euclidean tesselations#7D".

Fundamental convex regular and uniform honeycombs in dimensions 3–10 (or 2-9)
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 10-honeycomb	{3^[10]}	δ₁₀	hδ₁₀	qδ₁₀
Uniform n-honeycomb	{3^[n]}	δ_n	hδ_n	qδ_n	1_k2 • 2_k1 • k₂₁

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