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

Abstract

We study the problem of existence of two affine-equivalent bar-and-joint frameworks in Euclidean $d$-space which have prescribed combinatorial structure and edge lengths. We prove that theoretically this problem is always solvable, but we cannot propose any practical algorithm for its solution.

6 pages

References in corpus (2)

• How to decide whether two convex octahedra are affinely equivalent using their natural developments only
• Recognition of affine-equivalent polyhedra by their natural developments