Quasi-transitive tilings of the plane

Tiling of a surface is acted upon by its automorphism group. The tilings with single vertex orbit, the transitive tilings, are well studied since antiquity. In this talk I will present a class of locally symmetric tilings of the plane that has finitely many orbits but not transitive. Along the way I will talk about some known and a few new results about locally symmetric and pseudo-symmetric tilings of the plane.