Title: Reconstructing polytopes from projections or sections
Speaker: Sergii Myroshnychenko (Graduate Student, Kent State University)
Abstract: We are going to discuss one of the open problems of geometric tomography about projections. Along with partial previous results, the proof of the problem below will be investigated.
Let 2 ≤ k ≤ d and let P and Q be two convex polytopes in E ^d . Assume that their projections, P|H, Q|H, onto every k-dimensional subspace H, are congruent. We will show that P and Q or P and – Q are translates of each other.
If the time permits, we also will discuss an analogous result for sections by showing that P=Q or P=−Q, provided the polytopes contain the origin in their interior and their sections, P∩H, Q∩H, by every k-dimensional subspace H, are congruent.