Naslov
Hypercube Embedding of Wythoffians

Autori
Deza, Michel ; Dutour Sikirić, Mathieu ; Shpectorov, Sergey

Izvornik
ARS Mathematica Contemporanea (1855-3966) 1 (2008), 1; 99-111

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Coxeter grupe ; umetanje
(Coxeter group ; embedding)

Sažetak
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 Hm and half-cubes 1/2 Hm. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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