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A141536 Orders, sorted, of embeddable Wythoffians in dimension 4. 0
5, 8, 16, 10, 30, 64, 120, 192, 384, 1152, 14400 (list; graph; refs; listen; history; text; internal format)



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.


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.


Sequence in context: A063731 A129316 A039752 * A314561 A314562 A065905

Adjacent sequences:  A141533 A141534 A141535 * A141537 A141538 A141539




Jonathan Vos Post, Aug 12 2008



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