  We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of
the kagome lattice) has entropically-driven long-range order at low
temperatures (including zero). We then present Monte Carlo simulations, using a
cluster algorithm, of the 3-state and 4-state models. The 3-state model has a
phase transition to the high-temperature disordered phase at v = e^J - 1 =
-0.860599 +- 0.000004 that appears to be in the universality class of the
3-state Potts ferromagnet. The 4-state model is disordered throughout the
physical region, including at zero temperature.
