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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 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.〔Regular and semi-regular polytopes III, p.318-319〕 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. () ! () |- !colspan=3|Coxeter-Dynkin diagrams by family |- | hδ2 | ''Apeirogon'' | | | |- | hδ3 | ''Alternated square tiling'' (Same as ) | h=t1 t0,2 | | |- | hδ4 | ''Alternated cubic honeycomb'' | h | | |- | hδ5 | ''16-cell tetracomb'' (Same as ) | h | | |- | hδ6 | ''5-demicube honeycomb'' | h | | |- | hδ7 | ''6-demicube honeycomb'' | h | | |- | hδ8 | ''7-demicube honeycomb'' | h | | |- | hδ9 | ''8-demicube honeycomb'' |h | | |- |colspan=6| |- | hδn | ''n-demicubic honeycomb'' |h |colspan=2|... |} == References == * Coxeter, H.S.M. ''Regular Polytopes'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 *# 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=; h=, h= *# 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, ISBN 978-0-471-01003-6 () * * (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', (Zeit. 200 (1988) 3-45 ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Alternated hypercubic honeycomb」の詳細全文を読む スポンサード リンク
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