  The coupled cluster method (CCM) is applied to a spin-half model at zero
temperature which interpolates between a triangular lattice antiferromagnet
(TAF) and a Kagome lattice antiferromagnet (KAF). The strength of the bonds
which connect Kagome lattice sites is J, and the strength of the bonds which
link the non-Kagome lattice sites to the Kagome lattice sites on an underlying
triangular lattice is J'. Our results are found to be highly converged, and our
best estimate for the ground-state energy per spin for the spin-half KAF (J'=0)
of -0.4252 constitutes one of the most accurate results yet found for this
model. The amount of classical ordering on the Kagome lattice sites is also
considered, and it is seen that this parameter goes to zero for values of J'
very close the KAF point. Further evidence is also presented for CCM critical
points which reinforce the conjecture that there is a phase near to the KAF
point which is much different to that near to the TAF point (J=J').
