  Triangular billiards whose angles are rational multiples of $\pi$ are one of
the simplest examples of pseudo-integrable models with intriguing classical and
quantum properties. We perform an extensive numerical study of spectral
statistics of eight quantized rational triangles, six belonging to the family
of right-angled Veech triangles and two obtuse rational triangles. Large
spectral samples of up to one million energy levels were calculated for each
triangle which permits to determine their spectral statistics with great
accuracy. It is demonstrated that they are of the intermediate type, sharing
some features with chaotic systems, like level repulsion and some with
integrable systems, like exponential tails of the level spacing distributions.
Another distinctive feature of intermediate spectral statistics is a finite
value of the level compressibility.
  The short range statistics such as the level spacing distributions, and
long-range statistics such as the number variance and spectral form factors
were analyzed in detail. An excellent agreement between the numerical data and
the model of gamma distributions is revealed.
