  Buczy\'{n}ska and Wi\'{s}niewski showed that for the Jukes Cantor binary
model of a 3-valent tree the Hilbert polynomial depends only on the number of
leaves of the tree and not on its shape. We ask if this can be generalized to
other group-based models. In this paper we consider the Kimura 3-parameter
model and show that the generalization of the statement about the Hilbert
polynomials to the Kimura 3-parameter model is not possible as the Hilbert
polynomial depends on the shape of a 3-valent tree.
