A Complete Classification of Tile-makers
نویسندگان
چکیده
We extend the study of Akiyama’s tile-makers: surfaces whose developments all tile the plane. First, we prove that the developments of Akiyama’s tile-makers are the prototiles that tile the plane isohedrally with rotation and without reflection. Second, we give a simple characterization of all closed (boundaryless) tile-makers and give three new tile-makers not known to Akiyama. Finally, we prove that the developments of tile-makers are the isohedral prototiles.
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