Adjoints of Projective Transformations and Face-Figures of Convex Polytopes

Abstract

When F is a proper face of a (convex) polytope P in a Euclidean space E, an F-figure of P is an intersection of sets P and H where H is a hyperplane strictly separating F from all vertices of sets P and F (which have a one to one relation). Here it is shown how, when the origin is interior to P, the combinatorial (and, in a sense, the projective) structure of P's F-figures can be described in terms of the boundary structure of the polar polytope P superscript 0. The main tool is the notion of the adjoint of a projective transformation and a basic formula relating adjoints to polars.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1976
Accession Number
ADA033970

Entities

People

  • Victor Klee

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Convex Bodies
  • Convex Sets
  • Geometry
  • Mathematics
  • Military Research
  • Projective Geometry
  • Theorems
  • Topology
  • United States
  • United States Government
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space