Computing invariants of hyperbolic Coxeter groups and polyhedra
Given a hyperbolic Coxeter group G and its associated polyhedron P, we are interested in computing different invariants of these two objects. Concerning P, we want to answer to the following questions: is it compact? has it finite volume? what is its f-vector? Regarding G, we would like to compute its Euler characteristic (which is related to the volume of P when the dimension is even), its growth series and growth rate and we want to know if it is arithmetic or not. We will explain explain how these questions can be answered using the Coxeter graph of P and see that these computations can be handled by a computer.