1,1

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.

Michel Deza, Mathieu Dutour and Sergey Shpectorov, Hypercube embedding of Wythoffians (replaced) v5, Aug 11, 2008.

Sequence in context: A063731 A129316 A039752 this_sequence A065905 A126695 A001082

Adjacent sequences: A141533 A141534 A141535 this_sequence A141537 A141538 A141539

fini,full,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 12 2008