  The strand symmetric model is a phylogenetic model designed to reflect the
symmetry inherent in the double-stranded structure of DNA. We show that the set
of known phylogenetic invariants for the general strand symmetric model of the
three leaf claw tree entirely defines the ideal. This knowledge allows one to
determine the vanishing ideal of the general strand symmetric model of any
trivalent tree. Our proof of the main result is computational. We use the fact
that the Zariski closure of the strand symmetric model is the secant variety of
a toric variety to compute the dimension of the variety. We then show that the
known equations generate a prime ideal of the correct dimension using
elimination theory.
