A141536 Orders, sorted, of embeddable Wythoffians in dimension 4.

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

Offset

1,1

Comments

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.

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