  The quantities C_4 and Theta_2,2,2 are as defined by Wanless, C_4 just the
number of 4-loops of a graph. The construction of this paper provides a
counterexample to a conjecture of Butera, Pernici, and the author about the
monomer-dimer entropy, lambda, of a regular bipartite lattice. The lattice we
construct is not a lattice graph in its most common definition.
