Intersecting All Edges of Centrally Symmetric Polyhedra by Planes.
Abstract
Motivated by information-theoretic problems P. E. O'Neil has recently investigated the question how many hyperplanes are needed to cut all edges of an n-cube. A similar problem is investigated in this report, restricting the dimension but generalizing the class of polytopes. It is established that if P is a centrally symmetric convex polyhedron in 3-space then it is impossible to intersect all the edges of P by any pair of planes that miss the vertices of P. However, there exist convex 3-polytopes without a center of symmetry, as well as centrally symmetric tessellations of the 2-sphere, in which all edges may be intersected by a suitable pair of planes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1972
- Accession Number
- AD0739711
Entities
People
- Branko Gruenbaum
Organizations
- University of Washington