Ghys discovered in 2006 that the periodic orbits of the modular flow are identical to the set of orbits of the Lorenz flow, studied by Birman and Williams. Thus, for example, these orbits are all prime knots, fibered, and have positive signature. This is the first result regarding the topological properties of closed geodesics on Hecke triangles, which are otherwise a well studied class. The results were obtained using a "template" for the flow, which reduces the original three dimensional flow to a much simpler two dimensional system. In the talk I will present a method for computing templates for geodesic flows on an infinite class of Hecke triangle groups. We will then use the arising templates to show that as knots, all closed geodesics corresponding to any of these groups are prime.