Dirichlet domains provide polyhedral fundamental domains for discrete subgroups of the isometries of hyperbolic space on the hyperbolic space. Selberg introduced a similar construction of a polyhedral fundamental domain for the action of discrete subgroups of the higher rank Lie group SL(n,R) on the projective model of the associated symmetric space. His motivation was to study uniform lattices, for which these domains are finite-sided. We will address the following question asked by Kapovich: for which Anosov subgroups are these domains finite-sided? Anosov subgroups are hyperbolic discrete subgroups satisfying strong dynamical properties that have infinite covolume in higher rank. We will first consider an example of an Anosov subgroup for which this fundamental domain can have infinitely many sides. We then provide a sufficient condition on a subgroup to ensure that the domain is finitely sided in a strong sense. This is joint work with Colin Davalo.