Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope describing a toric variety associated to the algebraic statistical model. In the case of Z 2 or Z 2 × Z 2 , these polytopes have applications in the field of phylogenetics. We provide a half-space representation for the m-claw tree where G = Z 2 × Z 2 , which corresponds to the Kimura-3 model of evolution.

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Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species-is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the data contains a phylogenetic signal that will be recovered with varying accuracy due to the quality of the method used, and the quality of the data.The input for distance-based inference methods is an element of a Euclidean space with coordinates indexed by the pairs of organisms. For several algorithms there exists a subdivision of this space into polyhedral cones such that inputs in the same cone return the same tree topology. The geometry of these cones has been used to analyze the inference algorithms. In this chapter, we model how input data points drawn from DNA sequences are distributed throughout Euclidean space in relation to the space of tree metrics, which in turn can also be described as a collection of polyhedral cones.