Quarter 8-cubic honeycomb - Misplaced Pages

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{4,3}, h₆{4,3}, {3,3}×{3} duoprism {3}×{3} duoprism
Vertex figure
Coxeter group	${\tilde {D}}_{8}$ ×2 = ]
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. Its facets are 8-demicubes h{4,3}, pentic 8-cubes h₆{4,3}, {3,3}×{3} and {3}×{3} 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, See p318
Klitzing, Richard. "7D Euclidean tesselations#7D".

v t e Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space	Family	${\tilde {A}}_{n-1}$	${\tilde {C}}_{n-1}$	${\tilde {B}}_{n-1}$	${\tilde {D}}_{n-1}$	${\tilde {G}}_{2}$ / ${\tilde {F}}_{4}$ / ${\tilde {E}}_{n-1}$
E	Uniform tiling	0	δ₃	hδ₃	qδ₃	Hexagonal
E	Uniform convex honeycomb	0	δ₄	hδ₄	qδ₄
E	Uniform 4-honeycomb	0	δ₅	hδ₅	qδ₅	24-cell honeycomb
E	Uniform 5-honeycomb	0	δ₆	hδ₆	qδ₆
E	Uniform 6-honeycomb	0	δ₇	hδ₇	qδ₇	2₂₂
E	Uniform 7-honeycomb	0	δ₈	hδ₈	qδ₈	1₃₃ • 3₃₁
E	Uniform 8-honeycomb	0	δ₉	hδ₉	qδ₉	1₅₂ • 2₅₁ • 5₂₁
E	Uniform 9-honeycomb	0	δ₁₀	hδ₁₀	qδ₁₀
E	Uniform 10-honeycomb	0	δ₁₁	hδ₁₁	qδ₁₁
E	Uniform (n-1)-honeycomb	0	δ_n	hδ_n	qδ_n	1_k2 • 2_k1 • k₂₁