Strongly Obtuse Rational Lattice Triangles

Abstract

We classify rational triangles which unfold to Veech surfaces when the largest angle is at least $\frac{3\pi }{4}$. When the largest angle is greater than $\frac{2\pi }{3}$, we show that the unfolding is not Veech except possibly if it belongs to one of six infinite families. Our methods include a criterion of Mirzakhani and Wright that built on work of Möller and McMullen, and in most cases show that the orbit closure of the unfolding cannot have rank 1.