In a given set S={A} of shapes (e.g. open sets in a topological space), some shapes may be congruent to one or more others. A subset R of S is called a set of prototiles of S, if

• the shapes in R are mutually non-congruent
• R is complete in the sense that each shape A in S is congruent to one shape in this subset R.

The elements of R are then called the prototiles of S.

Of course any such subset R of S contains the same number of shapes. This number is called the number of prototiles of S.