Does anyone know of a catalog of sorts for what shapes are allowed for tiling a circular disk? For example, if you are allowed one piece to tile the disk, are all the possibilities essentially "pie"-shaped wedges, like these examples below? ...where all the pieces meet at a common point at the center of the circle, and all the pieces have an edge which makes up the circumference of the disk? Are all one-piece tilings rotationally symmetric? Or are there other possibilities of exactly covering the disk with a single tile? What about for two or more different tiles? Is there a better set of terms I should use in my search?
I found one example of a tessellation that doesn't use sectors.
Not sure if there are others, but that might give you ideas.