Naslov
Wythoff construction and L1-embedding

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

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
Geometric linearization of graphs and groups / - , 2007

Skup
International conference on Embeddings of Graphs and Groups into Hilbert and Banach spaces with applications

Mjesto i datum
Lausanne, Švicarska, 22.01.2007. - 26.01.2007

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Embedding; Wythoff construction

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. 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

POVEZANOST RADA