Normality of the Kimura 3-parameter model

Tree model is one of the central objects in phylogenetics. A group-based model is a tree model where the input parameters are $G$-invariant. We will discuss mainly Kimura 3-parameter model which is a group model with underlying group $\text{Mathbb}{Z}_2\times \text{Mathbb}{Z}_2$. The varieties associated to this model are toric and there is an explicit description by family of polytopes associated to these varieties. Thus one can study properties of these varieties by studying properties of family of polytopes. We show normality of these polytopes meaning that the associated projective toric varieties are projectively normal.