  A bar-and-joint framework is a finite set of points together with specified
distances between selected pairs. In rigidity theory we seek to understand when
the remaining pairwise distances are also fixed. If there exists a pair of
points which move relative to one another while maintaining the given distance
constraints, the framework is flexible; otherwise, it is rigid.
  Counting conditions due to Maxwell give a necessary combinatorial criterion
for generic minimal bar-and-joint rigidity in all dimensions. Laman showed that
these conditions are also sufficient for frameworks in R^2. However, the
flexible "double banana" shows that Maxwell's conditions are not sufficient to
guarantee rigidity in R^3. We present a generalization of the double banana to
a family of hyperbananas. In dimensions 3 and higher, these are
(infinitesimally) flexible, providing counterexamples to the natural
generalization of Laman's theorem.
