  In this paper we consider the class of graphs which are redundantly $d$-rigid
and $(d+1)$-connected but not globally $d$-rigid, where $d$ is the dimension.
This class arises from counterexamples to a conjecture by Bruce Hendrickson. It
seems that there are relatively few graphs in this class for a given number of
vertices. Using computations we show that $K_{5,5}$ is indeed the smallest
counterexample to the conjecture.
