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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1976
- Accession Number
- ADA033970
Entities
People
- Victor Klee
Organizations
- University of Washington