A ** tiling** or

called ** tiles**, in such a manner that:

In other words, the plane is completely covered by nonoverlapping tiles.

There is no requirement that the tiles be related in any way, but our interest is primarily in tilings where there are only a finite number of differently shaped tiles. A tessellation is of ** order-k**, or

The members of *S* are called ** prototiles**, and we say that

The most natural question is “Which polygons are monohedral prototiles?” The words ** monohedral, dihedral**, and

It is not difficult to see that every parallelogram tiles the plane, as in (a) below.

As a consequence, every triangle tiles the plane because two copies ...

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