English

On recognizing shapes of polytopes from their shadows

Metric Geometry 2018-11-14 v2

Abstract

Let PP and QQ be two convex polytopes both contained in the interior of an Euclidean ball rBdr\textbf{B}^{d}. We prove that P=QP=Q provided that their sight cones from any point on the sphere rSd1rS^{d-1} are congruent. We also prove an analogous result for spherical projections.

Keywords

Cite

@article{arxiv.1709.07083,
  title  = {On recognizing shapes of polytopes from their shadows},
  author = {Sergii Myroshnychenko},
  journal= {arXiv preprint arXiv:1709.07083},
  year   = {2018}
}
R2 v1 2026-06-22T21:49:59.111Z