  The bounce spectrum of a polygonal billiard table is the collection of all
bi-infinite sequences of edge labels corresponding to billiard trajectories on
the table. We give methods for reconstructing from the bounce spectrum of a
polygonal billiard table both the cyclic ordering of its edge labels and the
sizes of its angles. We also show that it is impossible to reconstruct the
exact shape of a polygonal billiard table from any finite collection of finite
words from its bounce spectrum.
