Quarter 8-cubic honeycomb

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.

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

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