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%I #7 Nov 21 2012 14:59:43
%S 5,8,16,10,30,64,120,192,384,1152,14400
%N Orders, sorted, of embeddable Wythoffians in dimension 4.
%C Sorted from Deza et al., Table 2, p.5. Abstract: The Wythoff construction takes a d-dimensional polytope P, a subset S of {0, . . ., d} and returns another d-dimensional polytope P(S). If P is a regular polytope, then P(S) is vertex-transitive. This construction builds a large part of the Archimedean polytopes and tilings in dimension 3 and 4. We want to determine, which of those Wythoffians P(S) with regular P have their skeleton or dual skeleton isometrically embeddable into the hypercubes H_m and half-cubes (1/2)H_m. We find six infinite series, which, we conjecture, cover all cases for dimension d > 5 and some sporadic cases in dimension 3 and 4 (see Tables 1 and 2).
%C Three out of those six infinite series are explained by a general result about the embedding of Wythoff construction for Coxeter groups. In the last section, we consider the Euclidean case; also, zonotopality of embeddable P(S) are addressed throughout the text.
%H Michel Deza, Mathieu Dutour and Sergey Shpectorov, <a href="http://arxiv.org/abs/math/0407527">Hypercube embedding of Wythoffians</a> arXiv:math/0407527 v5, Aug 11, 2008.
%K fini,full,nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 12 2008
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