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A141536
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Orders, sorted, of embeddable Wythoffians in dimension 4.
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0
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5, 8, 16, 10, 30, 64, 120, 192, 384, 1152, 14400
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OFFSET
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1,1
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COMMENTS
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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).
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.
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LINKS
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Table of n, a(n) for n=1..11.
Michel Deza, Mathieu Dutour and Sergey Shpectorov, Hypercube embedding of Wythoffians arXiv:math/0407527 v5, Aug 11, 2008.
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CROSSREFS
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Sequence in context: A063731 A129316 A039752 * A065905 A126695 A001082
Adjacent sequences: A141533 A141534 A141535 * A141537 A141538 A141539
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KEYWORD
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fini,full,nonn
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AUTHOR
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Jonathan Vos Post, Aug 12 2008
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STATUS
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approved
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