  We examine the topological order in the resonating singlet valence plaquette
(RSVP) phase of the hard-core quantum plaquette model (QPM) on the face
centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type
Hamiltonian of local plaquette resonances. This model is shown to exhibit a
$\mathbb{Z}_3$ topological order, which we show by identifying a $\mathbb{Z}_3$
topological constant (which leads to a $3^3$-fold topological ground state
degeneracy on the $3$-torus) and topological point-like charge and loop-like
magnetic excitations which obey $\mathbb{Z}_3$ statistics. We also consider an
exactly solvable generalization of this model, which makes the geometrical
origin of the $\mathbb{Z}_3$ order explicitly clear. For other models and
lattices, such generalizations produce a wide variety of topological phases,
some of which are novel fracton phases.
