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

1991; Wiley; Volume: 38; Issue: 2 Linguagem: Inglês

10.1112/s0025579300006707

2041-7942

Károly Bezdek,

Mathematics and Applications

MathematikaVolume 38, Issue 2 p. 362-375 Research Article The problem of illumination of the boundary of a convex body by affine subspaces Károly Bezdek, Károly Bezdek Dept. of Geometry, Eötvös L. University, 1088 Budapest, Rákóczi út 5, HungarySearch for more papers by this author Károly Bezdek, Károly Bezdek Dept. of Geometry, Eötvös L. University, 1088 Budapest, Rákóczi út 5, HungarySearch for more papers by this author First published: 01 December 1991 https://doi.org/10.1112/S0025579300006707Citations: 17AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat 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. Citing Literature Volume38, Issue2December 1991Pages 362-375 RelatedInformation