Themes and shapes in Oswald basic patterns (Q1200962)

Using connecting segments of vertices in regular tilings of the plane (e.g. by means of triangles and squares of side length 1) and suitable symmetry groups, one can generate patterns which are interesting with respect to their aesthetic and symmetry properties. The idea of such generations goes back to \textit{W. Ostwald} [Harmonie der Formen, Leipzig (1922) und Welt der Formen, Leipzig (1922-1925)]. The author gives a collection of interesting combinatorial statements on such patterns, and their basic symmetry properties are described, too. For further reading in that direction one can consult \textit{J. Flachsmeyer} [Die ``gesetzlich- schönen Gebilde'' Wissenschaft und Fortschritt 39, No. 7, 167-172 (1989)].