  We show that the spacing distributions of rational rhombus billiards fall in
a family of universality classes distinctly different from the Wigner-Dyson
family of random matrix theory and the Poisson distribution. Some of the
distributions find explanation in a recent work of Bogomolny, Gerland and
Schmit. For the irrational billiards, despite ergodicity, we get the same
distributions for the examples considered - once again, distinct from the
Wigner-Dyson distributions. All results are obtained numerically by a method
that allows us to reach very high energies.
