Hypercube embedding of Wythoffians
| dc.creator | Deza, Michel | |
| dc.creator | Dutour, Mathieu | |
| dc.creator | Shpectorov, Sergey | |
| dc.date | 2004-07-30 | |
| dc.date | 2008-08-11 | |
| dc.date.accessioned | 2026-07-07T09:55:44Z | |
| dc.date.available | 2026-07-07T09:55:44Z | |
| dc.description | 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 \ref{WythoffEmbeddable3} and \ref{WythoffEmbeddable4}). 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. | |
| dc.description | 12 pages, 6 tables | |
| dc.identifier | https://arxiv.org/abs/math/0407527 | |
| dc.identifier | http://arxiv.org/abs/math/0407527 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166735 | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.title | Hypercube embedding of Wythoffians | |
| dc.type | text |