Accession Number : AD0739711

Title :   Intersecting All Edges of Centrally Symmetric Polyhedra by Planes.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Gruenbaum,Branko

Report Date : APR 1972

Pagination or Media Count : 14

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)

Descriptors :   (*TOPOLOGY, *CONVEX SETS), TRANSFORMATIONS(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE