

A141536


Orders, sorted, of embeddable Wythoffians in dimension 4.


0



5, 8, 16, 10, 30, 64, 120, 192, 384, 1152, 14400
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OFFSET

1,1


COMMENTS

Sorted from Deza et al., Table 2, p.5. Abstract: The Wythoff construction takes a ddimensional polytope P, a subset S of {0, . . ., d} and returns another ddimensional polytope P(S). If P is a regular polytope, then P(S) is vertextransitive. 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 halfcubes (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.


LINKS

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.


CROSSREFS

Sequence in context: A063731 A129316 A039752 * A314561 A314562 A065905
Adjacent sequences: A141533 A141534 A141535 * A141537 A141538 A141539


KEYWORD

fini,full,nonn


AUTHOR

Jonathan Vos Post, Aug 12 2008


STATUS

approved



