  We study the ground state of hard-core bosons with nearest-neighbor hopping
and nearest-neighbor interactions on the triangular and Kagom\'e lattices by
mapping to a system of spins ($S={1\over2}$), which we analyze using spin-wave
theory. We find that the both lattices display superfluid and supersolid (a
coexistence of superfluid and solid) order as the parameters and filling are
varied. Quantum fluctuations seem large enough in the Kagom\'e system to raise
the interesting possibility of a disordered ground state.
