  In this note we study the uniqueness problem for collections of pennies and
marbles. More generally, consider a collection of unit $d$-spheres that may
touch but not overlap. Given the existence of such a collection, one may
analyse the contact graph of the collection. In particular we consider the
uniqueness of the collection arising from the contact graph. Using the language
of graph rigidity theory, we prove a precise characterisation of uniqueness
(global rigidity) in dimensions 2 and 3 when the contact graph is additionally
chordal. We then illustrate a wide range of examples in these cases. That is,
we illustrate collections of marbles and pennies that can be perturbed
continuously (flexible), are locally unique (rigid) and are unique (globally
rigid). We also contrast these examples with the usual generic setting of graph
rigidity.
