Discrete & Computational Geometry

, Volume 62, Issue 4, pp 856–864 | Cite as

On Recognizing Shapes of Polytopes from Their Shadows

  • Sergii MyroshnychenkoEmail author


Let P and Q be two convex polytopes both contained in the interior of a Euclidean ball \(r\mathbf B ^{d}\). We prove that \(P=Q\) provided that their sight cones from any point on the sphere \(rS^{d-1}\) are congruent. We also prove an analogous result for spherical projections.


Convex geometry Geometric tomography Projections of convex bodies Shadow picture Isoptic characterization 



The author is very grateful the anonymous referees for their suggestions that greatly improved the manuscript; and also to Vlad Yaskin and Dmitry Ryabogin for many fruitful and interesting discussions.


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Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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