An alternated square tiling or checkerboard pattern. or
An expanded square tiling.
A partially filled alternated cubic honeycomb with tetrahedral and octahedral cells. or
A subsymmetry colored alternated cubic honeycomb.
In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation. It is given a Schläfli symbol h{4,3...3,4} representing the regular form with half the vertices removed and containing the symmetry of Coxeter group for n ≥ 4. A lower symmetry form can be created by removing another mirror on an order-4 peak.[1]
The alternated hypercube facets become demihypercubes, and the deleted vertices create new orthoplex facets. The vertex figure for honeycombs of this family are rectified orthoplexes.
These are also named as hδn for an (n-1)-dimensional honeycomb.
pp. 122–123, 1973. (The lattice of hypercubes γn form the cubic honeycombs, δn+1)
pp. 154–156: Partial truncation or alternation, represented by h prefix: h{4,4}={4,4}; h{4,3,4}={31,1,4}, h{4,3,3,4}={3,3,4,3}
p. 296, Table II: Regular honeycombs, δn+1
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN978-0-471-01003-6[1]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
alternated, hypercubic, honeycomb, alternated, square, tiling, checkerboard, pattern, expanded, square, tiling, partially, filled, alternated, cubic, honeycomb, with, tetrahedral, octahedral, cells, subsymmetry, colored, alternated, cubic, honeycomb, geometry,. An alternated square tiling or checkerboard pattern or An expanded square tiling A partially filled alternated cubic honeycomb with tetrahedral and octahedral cells or A subsymmetry colored alternated cubic honeycomb In geometry the alternated hypercube honeycomb or demicubic honeycomb is a dimensional infinite series of honeycombs based on the hypercube honeycomb with an alternation operation It is given a Schlafli symbol h 4 3 3 4 representing the regular form with half the vertices removed and containing the symmetry of Coxeter group B n 1 displaystyle tilde B n 1 for n 4 A lower symmetry form D n 1 displaystyle tilde D n 1 can be created by removing another mirror on an order 4 peak 1 The alternated hypercube facets become demihypercubes and the deleted vertices create new orthoplex facets The vertex figure for honeycombs of this family are rectified orthoplexes These are also named as hdn for an n 1 dimensional honeycomb hdn Name Schlaflisymbol Symmetry family B n 1 displaystyle tilde B n 1 4 3n 4 31 1 D n 1 displaystyle tilde D n 1 31 1 3n 5 31 1 Coxeter Dynkin diagrams by family hd2 Apeirogon hd3 Alternated square tiling Same as 4 4 h 4 4 t1 4 4 t0 2 4 4 hd4 Alternated cubic honeycomb h 4 3 4 31 1 4 hd5 16 cell tetracomb Same as 3 3 4 3 h 4 32 4 31 1 3 4 31 1 1 1 hd6 5 demicube honeycomb h 4 33 4 31 1 32 4 31 1 3 31 1 hd7 6 demicube honeycomb h 4 34 4 31 1 33 4 31 1 32 31 1 hd8 7 demicube honeycomb h 4 35 4 31 1 34 4 31 1 33 31 1 hd9 8 demicube honeycomb h 4 36 4 31 1 35 4 31 1 34 31 1 hdn n demicubic honeycomb h 4 3n 3 4 31 1 3n 4 4 31 1 3n 5 31 1 References edit Regular and semi regular polytopes III p 318 319 Coxeter H S M Regular Polytopes 3rd edition 1973 Dover edition ISBN 0 486 61480 8 pp 122 123 1973 The lattice of hypercubes gn form the cubic honeycombs dn 1 pp 154 156 Partial truncation or alternation represented by h prefix h 4 4 4 4 h 4 3 4 31 1 4 h 4 3 3 4 3 3 4 3 p 296 Table II Regular honeycombs dn 1 Kaleidoscopes Selected Writings of H S M Coxeter editied 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 vteFundamental convex regular and uniform honeycombs in dimensions 2 9 Space Family A n 1 displaystyle tilde A n 1 nbsp C n 1 displaystyle tilde C n 1 nbsp B n 1 displaystyle tilde B n 1 nbsp D n 1 displaystyle tilde D n 1 nbsp G 2 displaystyle tilde G 2 nbsp F 4 displaystyle tilde F 4 nbsp E n 1 displaystyle tilde E n 1 nbsp E2 Uniform tiling 3 3 d3 hd3 qd3 Hexagonal E3 Uniform convex honeycomb 3 4 d4 hd4 qd4 E4 Uniform 4 honeycomb 3 5 d5 hd5 qd5 24 cell honeycomb E5 Uniform 5 honeycomb 3 6 d6 hd6 qd6 E6 Uniform 6 honeycomb 3 7 d7 hd7 qd7 222 E7 Uniform 7 honeycomb 3 8 d8 hd8 qd8 133 331 E8 Uniform 8 honeycomb 3 9 d9 hd9 qd9 152 251 521 E9 Uniform 9 honeycomb 3 10 d10 hd10 qd10 E10 Uniform 10 honeycomb 3 11 d11 hd11 qd11 En 1 Uniform n 1 honeycomb 3 n dn hdn qdn 1k2 2k1 k21 Retrieved from https en wikipedia org w index php title Alternated hypercubic honeycomb amp oldid 782229215, wikipedia, wiki, book, books, library,
