ABSTRACT
In this chapter we discuss the concept of global rigidity for bar and joint frameworks in an arbitrary fixed dimension, d. This is stronger than the plain “rigidity” property (also called local rigidity), in that it requires that, up to congruence, there is a unique framework satisfying the given length constraints. In particular, even if there are a only finite number of equivalent and noncongruent frameworks, if that number is greater than one, then such frameworks are not considered to be globally rigid.
