Crystallographic reptiles

Research paper by Götz Gelbrich

Indexed on: 01 Jul '94Published on: 01 Jul '94Published in: Geometriae Dedicata


We consider tilings ofRn 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.