  We study phase transitions of the Potts model on the centered-triangular
lattice with two types of couplings, namely $K$ between neighboring triangular
sites, and $J$ between the centered and the triangular sites. Results are
obtained by means of a finite-size analysis based on numerical transfer matrix
calculations and Monte Carlo simulations. Our investigation covers the whole
$(K, J)$ phase diagram, but we find that most of the interesting physics
applies to the antiferromagnetic case $K<0$, where the model is geometrically
frustrated. In particular, we find that there are, for all finite $J$, two
transitions when K is varied. Their critical properties are explored. In the
limits $J\to \pm \infty$ we find algebraic phases with infinite-order
transitions to the ferromagnetic phase.
