  This paper is concerned with physics of the low energy singlet excitations
found to exist below the spin gap in numerical studies of the Kagome lattice
quantum Heisenberg antiferromagnet. Insight into the nature of these
excitations is obtained by exploiting an approximate mapping to a fully
frustrated transverse field Ising model on the dual dice lattice. This Ising
model is shown to possess at least two phases - an ordered phase that also
breaks translational symmetry with a large unit cell, and a paramagnetic phase.
The former is argued to be a likely candidate for the ground state of the
original Kagome magnet which thereby exhibits a specific pattern of dimer
ordering with a large unit cell. Comparisons with available numerical results
are made.
