The geometric cone relations for simplicial and cubical complexes
type: Item
instance of: scholarly article
title: The geometric cone relations for simplicial and cubical complexes
zbMATH Open document ID: 0896.52020
DOI: 10.1016/S0012-365X(97)00075-7
author: Beifang Chen
author: Min Yan
published in: Discrete Mathematics
publication date: 1998-03-18T00:00:00Z
review text: It is well-known that the Dehn-Sommerville equations are the only (linear) (independent) relations on the \(f\)-vectors for convex simplicial polytopes, and recently B. F. Chen generalized them to cone relations for simplicial and cubical polytopes, where the angle-sum relations of Perles and Shephard follow easily from the numerical form of these cone relations. The authors derive analogues of these relations for simplicial and cubical complexes, both in cone functions and angles.
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 1130764
zbMATH Keywords: simplicial polytopes
zbMATH Keywords: simplicial complexes
zbMATH Keywords: regular decomposition
zbMATH Keywords: Dehn-Sommerville equations
zbMATH Keywords: cubical polytopes
zbMATH Keywords: angle-sum relations
zbMATH Keywords: cubical complexes
reviewed by: Horst Martini
MaRDI profile type: Publication
cites work: The Gram-Sommerville and Gauss-Bonnet theorems and combinatorial geometric measures for noncompact polyhedra
cites work: The incidence algebra of polyhedra over the Minkowski algebra
cites work: The geometric Dehn-Sommerville relations
cites work: Q5547252
cites work: Angle‐sum relations for polyhedral sets
cites work: Angle Sums of Convex Polytopes.
cites work: Lectures on Polytopes
full work available at URL: s0012-365x(97)00075-7
OpenAlex ID: W2136784154
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description: scientific article; zbMATH DE number 1130764