  We prove the existence of long-range order at sufficiently low temperatures,
including zero temperature, for the three-state Potts antiferromagnet on a
class of quasi-transitive plane quadrangulations, including the diced lattice.
More precisely, we show the existence of (at least) three infinite-volume Gibbs
measures, which exhibit spontaneous magnetization in the sense that vertices in
one sublattice have a higher probability to be in one state than in either of
the other two states. For the special case of the diced lattice, we give a good
rigorous lower bound on this probability, based on computer-assisted
calculations that are not available for the other lattices.
