either the transformation of each of the two tiles separately (example below with concave tiles). either the transformation of the two tile set Translation as in the present case, we try the first: this gives us two tiles. When we have several kinds of transformations before Shephard in their book Tilings and Patterns. The symmetry group used is that of the International Tables for x-ray crystallography. Designation R3 R3 R3 R3 R3 R3:Īnd its transformations before translations The base polygon of the 'madman' is a regular hexagon. We will refer it by R3S R3S R3S R3S because the sides are both of 3 rotations and symmetries: The one of the duck is a rhomb with two angles of 120°. Now here are the designations of basic polygons for: We will designate it by the isometries of the sides, that is to say R2 R4 R4:
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