  We find a simple spin Hamiltonian to describe physical states of $2+1$
dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation
of the electric field representation at $j_{\rm max}=\frac{1}{2}$. The simple
spin Hamiltonian only contains local products of Pauli matrices, even though
Gauss's law has been completely integrated out.
