In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4} or Coxeter symbol qδ<sub>4</sub> representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group for n âÂÂ¥ 5, with = and for quarter n-cubic honeycombs = .
See also
References
- Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition,
- # pp. 122âÂÂ123, 1973. (The lattice of hypercubes γ<sub>n</sub> form the cubic honeycombs, δ<sub>n+1</sub>)
- # pp. 154âÂÂ156: Partial truncation or alternation, represented by q prefix
- # p. 296, Table II: Regular honeycombs, δ<sub>n+1</sub>
- 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 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
- (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