  We discuss the phase diagram of the quantum dimer model on the hexagonal
(honeycomb) lattice. In addition to the columnar and staggered valence bond
solids which have been discussed in previous work, we establish the existence
of a plaquette valence bond solid. The transition between the plaquette and
columnar phases at $v/t=-0.2 \pm 0.05$ is argued to be first order. We note
that this model should describe valence bond dominated phases of frustrated
Heisenberg models on the hexagonal lattice and discuss its relation to recent
exact diagonalisation work by J.B. Fouet etal on the J_1-J_2 model on the same
lattice. Our results also shed light on the properties of the transverse field
Ising antiferromagnet on the triangular lattice and the classical Ising
antiferromagnet on the stacked triangular lattice, which are related to dimer
models by duality.
