Geodesic
On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width
Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 342-348

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DOI

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.
DOI : 10.4153/CMB-2009-037-0
Mots-clés : 52A20, 52A37, 52C17, 52C35, almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray Conjecture 
Bezdek, K.; Kiss, Gy. On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width. Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 342-348. doi: 10.4153/CMB-2009-037-0
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     title = {On the {X-ray} {Number} of {Almost} {Smooth} {Convex} {Bodies} and of {Convex} {Bodies} of {Constant} {Width}},
     journal = {Canadian mathematical bulletin},
     pages = {342--348},
     year = {2009},
     volume = {52},
     number = {3},
     doi = {10.4153/CMB-2009-037-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-037-0/}
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