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	[math]\displaystyle{ {\tilde{D}}_8 }[/math]×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. 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

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 [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". https://bendwavy.org/klitzing/dimensions/flat.htm. 

Fundamental convex regular and uniform honeycombs in dimensions 2-9
Space	Family	[math]\displaystyle{ {\tilde{A}}_{n-1} }[/math]	[math]\displaystyle{ {\tilde{C}}_{n-1} }[/math]	[math]\displaystyle{ {\tilde{B}}_{n-1} }[/math]	[math]\displaystyle{ {\tilde{D}}_{n-1} }[/math]	[math]\displaystyle{ {\tilde{G}}_2 }[/math] / [math]\displaystyle{ {\tilde{F}}_4 }[/math] / [math]\displaystyle{ {\tilde{E}}_{n-1} }[/math]
E2	Uniform tiling	{3[3]}	δ3	hδ3	qδ3	Hexagonal
E3	Uniform convex honeycomb	{3[4]}	δ4	hδ4	qδ4
E4	Uniform 4-honeycomb	{3[5]}	δ5	hδ5	qδ5	24-cell honeycomb
E5	Uniform 5-honeycomb	{3[6]}	δ6	hδ6	qδ6
E6	Uniform 6-honeycomb	{3[7]}	δ7	hδ7	qδ7	222
E7	Uniform 7-honeycomb	{3[8]}	δ8	hδ8	qδ8	133 • 331
E8	Uniform 8-honeycomb	{3[9]}	δ9	hδ9	qδ9	152 • 251 • 521
E9	Uniform 9-honeycomb	{3[10]}	δ10	hδ10	qδ10
En-1	Uniform (n-1)-honeycomb	{3[n]}	δn	hδn	qδn	1k2 • 2k1 • k21