Recognition of affine-equivalent polyhedra by their natural developments

Abstract

The classical Cauchy rigidity theorem for convex polytopes reads that if two convex polytopes have isometric developments then they are congruent. In other words, we can decide whether two polyhedra are isometric or not by using their developments only. In this article, we study a similar problem about whether it is possible, using only the developments of two convex polyhedra of Euclidean 3-space, to understand that these polyhedra are (or are not) affine-equivalent.

21 pages, 4 figures; this v4 is an English translation of v3 which is in Russian

References in corpus (2)

• New efficient algorithm for the isometric embedding of 2-surface metrics in 3 dimensional Euclidean space
• How to decide whether two convex octahedra are affinely equivalent using their natural developments only

Cited by in corpus (1)

• On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$-space