SO(2)-congruent projections of convex bodies with rotation about the origin

Abstract

We prove that if two convex bodies $K,L\subset {\mathbb{R}}^3$ satisfy the property that the orthogonal projections of $K$ and $L$ onto every plane containing the origin are roations of each other, then either $K$ and $L$ coincide or $L$ is the image of $K$ under a reflection about the origin

arXiv comment6 pages, 1 figure