Abstract
We consider tilings ofR n by copies of a compact setA under the action of a crystallographic group, such that the union ofk suitably chosen tiles is affinely isomorphic toA. For dimensionn=2 we show that for eachk≥2 there is a finite number of isomorphy classes of such setsA which are homeomorphic to a disk. We give an algorithm which determines all disk-like tiles for a given group and numberk. The algorithm will be applied to the groupsp2 andp3 withk=3.
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