We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices include the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer liquid. These models offer a very natural-and maybe the simplest possible-framework to illustrate general concepts such as fractionalization, topological order, and relation to Z2 gauge theories.
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