publication . Preprint . Article . 2008

Hypercube embedding of Wythoffians

Michel Marie Deza; Mathieu Dutour Sikirić; Sergey Shpectorov;
Open Access English
  • Published: 22 Aug 2008
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} a...
arXiv: Mathematics::Metric GeometryMathematics::Combinatorics
free text keywords: Mathematics - Combinatorics, Mathematics - Geometric Topology, Coxeter group, Polytope, Uniform polytope, Topology, Discrete mathematics, Cross-polytope, Uniform k 21 polytope, Regular polytope, Hypercube, Combinatorics, Wythoff construction, Mathematics
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publication . Preprint . Article . 2008

Hypercube embedding of Wythoffians

Michel Marie Deza; Mathieu Dutour Sikirić; Sergey Shpectorov;