Graphs and Dual Graphs of Abstract Polytopes

Abstract

A general and convenient framework for investigating the combinatorial structure of simple polytopes is given by a set of three axioms (proposed by G. B. Dantzig) which define abstract polytopes. These axioms are discussed and it is shown that, combinatorially, simple polytopes constitute a proper subclass of abstract polytopes. The purpose of the paper is to study the graphs and dual graphs of abstract polytopes and in particular, to show that some well-known properties of graphs of polytopes are satisfied also by the graphs and dual graphs of abstract polytopes.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0732435

Entities

People

  • Ilan Adler

Organizations

  • University of California, Berkeley

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Fields of Study

  • Geography
  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.