The Petersen Polytopes.

Abstract

A facet of a convex polytope C is the intersection of C with a supporting hyperplane. Since the extreme points (extrema) of a facet F of C are just the extreme of C that lie in F, a facet is completely described by the list of its extrema. In the following we may not distinguish among: (a) a polytope; (b) the set of extrema of the polytope; (c) the set of coordinate vectors of the extrema of the polytope; (d) the set of vertices of the graph G corresponding to the rows of Z that are coordinate vectors of the extrema of the polytope. If EZ is singular, then W = conv (w sub i : i an element of U) is not a facet.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1986
Accession Number
ADA182390

Entities

People

  • David L. Powers

Organizations

  • Clarkson University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Computer Science
  • Computers
  • Construction
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Mathematics
  • Permutations
  • Polynomials

Readers

  • Graph Algorithms and Convex Optimization.