Ghys discovered in 2006 that the periodic orbits of the modular flow posess unique topological properties. For example, these orbits are all prime knots, fibered, and have positive signature. These are pioneer results regarding the topological aspects of closed geodesics on hyperbolic surfaces and orbifolds. 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 for these groups are prime.