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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.
