Limit distribution of the nodal domain number for the right-isosceles triangle billiard

We present the probability distribution function of the nodal domain number for the right-isosceles triangle billiard. This is the first explicit result for a nonseparable plane polygonal billiard. The distribution function has a peak at $2/\pi$ (the same as for integrable billiards) and also at $2\sqrt{2}/\pi$. The only exact results previously known in this direction correspond to integrable billiards that are separable.