Cutting a Polytope

Abstract

We show that given two vertices of a polytope one cannot in general find a hyperplane containing the vertices that has two or more facets of the polytope in one closed half-space. Our result refutes a long-standing conjecture. We prove the result by constructing a 4-dimensional polytope that provides the counterexample. Also, we show that such a cutting hyperplane can be found for each pair of vertices, if the polytope is either simplicial or 3- dimensional.

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Document Details

Document Type
Technical Report
Publication Date
May 15, 1990
Accession Number
AD1020178

Entities

People

  • Nagabhushana Prabhu
  • William Jockusch

Organizations

  • Courant Institute of Mathematical Sciences, NYU

Tags

DTIC Thesaurus Topics

  • Geometry
  • Mathematics
  • Physical Properties
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space