Polytopes which are orthogonal projections of regular simplexes
type: Item
instance of: scholarly article
title: Polytopes which are orthogonal projections of regular simplexes
zbMATH Open document ID: 0722.52007
DOI: 10.1007/BF00147736
author: Toshio Kawashima
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: The author discusses the class \(P_{m,n}\) of convex n-polytopes in \({\mathbb{R}}^ n\) with m vertices which are certain orthogonal projections of regular simplices. The members in \(P_{m,n}\) are called \(\pi\)- polytopes. Every sufficiently symmetric polytope is an example of a \(\pi\)-polytope. The author proves that there exists a one-to-one correspondence (``duality'') between the polytopes in \(P_{m,n}\) and those in \(P_{m,m-n-1}\) which preserves the symmetry groups. Also it is shown that a \(\pi\)-polytope is an orthogonal projection of a crosspolytope if and only if it has central symmetry.
reviewed by: Egon Schulte
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 4190575
zbMATH Keywords: convex n-polytopes
zbMATH Keywords: orthogonal projections of regular simplices
zbMATH Keywords: symmetric polytope
zbMATH Keywords: crosspolytope
zbMATH Keywords: central symmetry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147736
OpenAlex ID: W2089946268
description: scientific article; zbMATH DE number 4190575