Lattice surfaces and smallest triangles

Abstract

We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than 1 20 is complete. In particular, this means that there are no new lattice surfaces for which the area of the smallest virtual triangle is greater than .05. Our method follows an algorithm described by Smillie and Weiss and improves on it in certain respects.