In a given set S of shapes, 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.

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