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On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width

Published online by Cambridge University Press:  20 November 2018

K. Bezdek  and
Gy. Kiss
K. Bezdek
Affiliation:
Department of Mathematics and Statistics, 2500 University Drive N.W., University of Calgary, AB, T2N 1N4 e-mail: bezdek@math.ucalgary.ca
Gy. Kiss
Affiliation:
Department of Geometry, Mathematical Institute, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary e-mail: kissgy@cs.elte.hu
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Abstract

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The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width of dimensions 3, 4, 5 and 6.

Keywords

52A2052A3752C1752C35almost smooth convex bodyconvex body of constant widthweakly neighbourly antipodal convex polytopeIllumination ConjectureX-ray numberX-ray Conjecture
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 3 , 01 September 2009 , pp. 342 - 348
Copyright
Copyright © Canadian Mathematical Society 2009

References

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