Construction of non-Wythoffian perfect \(4\)-polytopes
type: Item
instance of: scholarly article
title: Construction of non-Wythoffian perfect \(4\)-polytopes
zbMATH Open document ID: 1036.52017
author: Gábor Gévay
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/230128
full work available at URL: 18.html
review text: Two convex polytopes \(P,Q\subset\mathbb R^d\) are symmetrically equivalent if there is an isometry \(\phi\) of \(\mathbb R^d\) and a combinatorial isomorphism \(\psi:P\to Q\) such that for each face \(F<P\) and each isometry \(\sigma\) fixing \(P\) we have that \(\sigma(F)=\psi^{-1}\phi^{-1}\sigma\phi\psi(F)\). A polytope is perfect if each symmetrically equivalent polytope is similar. Perfect polytopes generalize regular polytopes, and further examples arise as special cases of Wythoff's construction, that is, as the convex hull of a point orbit under a finite reflection group. The author constructs \(4\)-dimensional polytopes which cannot be obtained by Wythoff's method.
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 52B15
zbMATH DE Number: 1894857
zbMATH Keywords: perfect polytopes
zbMATH Keywords: Wythoff construction
zbMATH Keywords: symmetrically equivalent polytope
zbMATH Keywords: 4-dimensional polytopes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1894857