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

  • Károly Bezdek (a1)

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.

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12. M. Lassak . Covering the boundary of a convex set by tiles. Proc. Amer. Math. Soc, 104 (1988), 269272.

13. F. W. Levi . Ein geometrisches Überdeckungsproblem. Arch. Math., 5 (1954), 476478.

14. F. W. Levi . Überdeckung eines Eibereiches durch Parallelverschiebungen seines offenen Kerns. Arch. Math., 6 (1955), 369370.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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