Title: Finding extreme rays via the fundamental domain

A fundamental domain of geometric object is a minimal subset D such that the object can be covered by isomorphs of D under the natural symmetry group of the object. For a convex polyhedral cone we have the property that every orbit of extreme rays has exactly one representative in a given fundamental domain. In this talk I will present some ideas and preliminary experiments for computing orbits of extreme rays of convex cones, via computing (approximately) a fundamental domain of the cone.