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- W2950545724 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 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." @default.
- W2950545724 created "2019-06-27" @default.
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- W2950545724 date "2004-07-30" @default.
- W2950545724 modified "2023-10-18" @default.
- W2950545724 title "Hypercube embedding of Wythoffians" @default.
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