Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8905030 | Advances in Mathematics | 2018 | 23 Pages |
Abstract
Let 2â¤kâ¤dâ1 and let P and Q be two convex polytopes in Ed. Assume that their projections, P|H, Q|H, onto every k-dimensional subspace H, are congruent. In this paper we show that P and Q or P and âQ are translates of each other. We also prove an analogous result for sections by showing that P=Q or P=âQ, provided the polytopes contain the origin in their interior and their sections, Pâ©H, Qâ©H, by every k-dimensional subspace H, are congruent.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Sergii Myroshnychenko, Dmitry Ryabogin,