In this paper we present geometric features of group-based phylogenetic models. We address a long standing problem of determining the ideal of the claw tree , . We focus on the 3-Kimura model. In particular we present a precise geometric description of the variety associated to any tree on a Zariski open set. This set contains all biologically meaningful points. The result confirms the conjecture of Sturmfels and Sullivant  on the degree in which the ideal associated to the 3-Kimura model is generated on that set.
- PHYLOGENETIC INVARIANTS