Quantization of the three dimensional Sinai billiard

For the first time a three--dimensional (3D) chaotic billiard -- the 3D Sinai billiard -- was quantized, and high--precision spectra with thousands of eigenvalues were calculated. We present here a semiclassical and statistical analysis of the spectra, and point out some of the features which are genuine consequences of the three dimensionality of this chaotic billiard.