You've seen these before. The Corian countertop and sink merge seamlessly. You often find them in hotels and restaurant bathrooms because they make clean-up so much easier. The Corian sink and counter are fused together in the factory.
But I've found that Corian sinks come in a wide range of styles, duplicating many of the styles you have seen in ceramic versions.
One interesting type of Corian sink is the recessed apron sink. An apron sink, sometimes called a farmhouse sink, is typically very deep--10 1/2", in many cases. The front of the apron sink is exposed, while the back three sides are hidden by the kitchen counter.
One iteration of the apron sink is the recessed apron sink, with a slight depression on the front to allow for the installation of tiles, if desired. In the American Standard Corian sink shown, four 6" x 6" tiles can be installed on the front apron.