
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 informationtheoretic problems P. E. O'Neil has recently investigated the question how many hyperplanes are needed to cut all edges of an ncube. 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 3space 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 3polytopes without a center of symmetry, as well as centrally symmetric tessellations of the 2sphere, 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