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):

Report Date:

1972-04-01

Pagination or Media Count:

14.0

Abstract:

Motivated by information-theoretic problems P. E. ONeil 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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE