  We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so
as to construct a concrete example of the model which exhibits the first-order
phase transition between different valence-bond solids suggested recently by
Batista and Trugman and look for the possibility of other exotic dimer states.
We show that our model contains three exotic valence-bond phases (herringbone,
checkerboard and dimer smectic) in the ground-state phase diagram and that it
realizes the phase transition from the staggered valence-bond solid to the
herringbone one. The checkerboard phase has four-fold rotational symmetry,
while the dimer smectic, in the absence of quantum fluctuations, has massive
degeneracy originating from partial ordering only in one of the two spatial
directions. A resonance process involving three dimers resolves this massive
degeneracy and dimer smectic gets ordered (order from disorder).
