Monohedral periodic tilings of the plane with any number of aspects (Q1182881)

Let \(\mathcal T\) be a tiling of the euclidean plane. An aspect of \(\mathcal T\) is a translation class of tiles; that is, the set of all tiles of \(\mathcal T\) which are translates of a given tile of \(\mathcal T\) (the translation may not preserve \(\mathcal T\)). A tiling \(\mathcal T\) is monohedral if its tiles are congruent to each other. It is proved that for any positive integer \(n\) there are monohedral (doubly) periodic tilings of the plane with exactly \(n\) aspects.