  We introduce a two dimensional network of corner-sharing triangles with
square lattice symmetry. Properties of magnetic systems here should be similar
to those on the kagome lattice. Focusing on the spin half Heisenberg quantum
antiferromagnet, we generalise the spin symmetry group from SU(2) to SU(N). In
the large N limit, we map the model exactly to the eight vertex model, solved
by Baxter. We predict an exponential number of low-lying singlet states, a
triplet gap, and a two-peak specific heat. In addition, the large N limit
suggests a finite temperature phase transition into a phase with ordered
``resonance loops'' and broken translational symmetry.
