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

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Károly Bezdek
Károly Bezdek
Affiliation:
Dept. of Geometry, Eötvös L. University, 1088 Budapest, Rákóczi út 5, Hungary
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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.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 362 - 375
Copyright
Copyright © University College London 1991

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