Mathematika

Research Article

The problem of illumination of the boundary of a convex body by affine subspaces

Károly Bezdeka1

a1 Dept. of Geometry, Eötvös L. University, 1088 Budapest, Rákóczi út 5, Hungary

Abstract

The main result of this paper is the following theorem. If P is a convex polytope of Ed with affine symmetry, then P can be illuminated by eight (d - 3)-dimensional affine subspaces (two (d- 2)-dimensional affine subspaces, resp.) lying outside P, where d ≥ 3. For d = 3 this proves Hadwiger's conjecture for symmetric convex polyhedra namely, it shows that any convex polyhedron with affine symmetry can be covered by eight smaller homothetic polyhedra. The cornerstone of the proof is a general separation method.

(Received November 01 1990)

Key Words:

  • 52A20: CONVEX AND DISCRETE GEOMETRY; General convexity; Convex sets in n-dimensions.

Key Words: