Puzzles and polytope isomorphisms
type: Item
instance of: scholarly article
title: Puzzles and polytope isomorphisms
zbMATH Open document ID: 0634.52005
DOI: 10.1007/BF01830678
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137246
review text: The authors call the set \(\pi\) \({\mathfrak C}\) of d- and (d-1)-cells of a simplicial d-complex \({\mathfrak C}\) its puzzle, and a puzzle isomorphism between two such complexes \({\mathfrak A},{\mathfrak B}\) is a bijection between \(\pi\) \({\mathfrak A}\) and \(\pi\) \({\mathfrak B}\) which preserves dimension and incidence. They use homological arguments to show that puzzle isomorphisms between the boundary complexes of simplicial polytopes extend to combinatorial isomorphisms between the polytopes, thus confirming (in the dual form) a conjecture of Perles.
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4032501
zbMATH Keywords: puzzle
zbMATH Keywords: simplicial polytopes
zbMATH Keywords: combinatorial isomorphisms
zbMATH Keywords: conjecture of Perles
Wikidata QID: Q29395940
author: Roswitha Blind
author: P. Mani-Levitska
MaRDI profile type: Publication
cites work: Shellable Decompositions of Cells and Spheres.
cites work: Q5643279
cites work: Q3889700
cites work: Spheres with few vertices
cites work: Neighborly polytopes
cites work: Einfache, konvexe Polytope und ihre Graphen
cites work: Q5522742
OpenAlex ID: W1985302945
description: scientific article; zbMATH DE number 4032501