  Given a group-based Markov model on a tree, one can compute the vertex
representation of a polytope which describes the associated toric variety. The
half-space representation, however, is not easily computable. In the case of
$\mathbb{Z}_2$ or $\mathbb{Z}_2\times\mathbb{Z}_2$, these polytopes have
applications in the field of phylogenetics. We provide a half-space
representation for the $m$-claw tree where $G=\mathbb{Z}_2\times\mathbb{Z}_2$,
which corresponds to the Kimura-3 model of evolution.
