  This paper considers aspects of a Kagome lattice system with states
classified by plane partitions. Using two sets of free fermions, we rewrite the
lattice in terms of two families of spin chains. In this formalism, the quantum
crystals Hamiltonian becomes more transparent, and we determine expressions for
the first 3 levels of plane partition states. A classical statistical model
associated with local configurations in the Kagome lattice is also defined, and
we show that a reduction of this classical system gives two Yang-Baxter
integrable subsystems analogous to a descendant of the 6-vertex model.
