  We determine the phase diagram of hardcore bosons on a triangular lattice
with nearest neighbor repulsion, paying special attention to the stability of
the supersolid phase. Similar to the same model on a square lattice we find
that for densities $\rho<1/3$ or $\rho>2/3$ a supersolid phase is unstable and
the transition between a commensurate solid and the superfluid is of first
order. At intermediate fillings $1/3 < \rho < 2/3$ we find an extended
supersolid phase even at half filling $\rho=1/2$.
