The global rigidity of a framework is not an affine-invariant property

Abstract

It is well-known that the property of a bar-and-joint framework `to be infinitesimally rigid' is invariant under projective transformations of Eucliean $d$-space for every $d\geqslant 2$. It is less known that the property of a bar-and-joint framework `to be globally rigid' is not invariant even under affine transformations of the Euclidean plane. In this note, we prove of the latter statement for Euclidean $d$-space for every $d\geqslant 2$.