Quarter 8-cubic honeycomb explained

bgcolor=#e7dcc3 colspan=2	quarter 8-cubic honeycomb
bgcolor=#ffffff align=center colspan=2	(No image)
Type	Uniform 8-honeycomb
Family	Quarter hypercubic honeycomb
Schläfli symbol	q
Coxeter diagram	=
7-face type	h, h6, × duoprism × duoprism
Vertex figure
Coxeter group	{\tilde{D}} _{8} ×2 = 3^1,1,3,3,3,3,3^1,1
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, pentic 8-cubes h₆, × and × 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, http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html
  • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318 https://books.google.com/books?id=fUm5Mwfx8rAC&dq=%22quarter+cubic+honeycomb%22+q%7B4%2C3%2C4%7D&pg=PA318

Notes and References

1. Coxeter, Regular and Semi-Regular Polytopes III, (1988), p318