Separation in and X-Raying of Convex Bodies

Date
2014-09-15
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Abstract
In this thesis, we introduce an algorithm to compute 6-dimensional totally-sewn neighbourly polytopes. We apply this algorithm to construct a class of semi-cyclic 6-polytopes, and give a complete description of their faces. We then confirm the Separation Conjecture for these semi-cyclic 6-polytopes. Next, we verify the X-ray Conjecture in the plane by showing that triangles are the only planar convex sets that cannot be X-rayed along two lines. We use this result to show that any 3-dimensional convex body exhibiting mirror symmetry also satisfies the X-ray conjecture.
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Mathematics
Citation
Trelford, R. G. (2014). Separation in and X-Raying of Convex Bodies (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27756