Strukturen geomerischer Ornamente. (Structures of geometric ornaments) (Q1104932)

The author studies double-periodic tilings of the Euclidean plane from the point of view of graph-theory. He introduces a symbol (``Tableau'') which collects information on local data of the tiling in terms of the valences of the vertices of the tiles in a fundamental domain. Analogues to Euler's theorem for periodic tilings are discussed, emphasizing graph- theoretical aspects. The reader is also referred to the recent book ``Tilings and Patterns'' by \textit{B. Grünbaum} and \textit{G. C. Shephard} (1987; Zbl 0601.05001). This provides a systematic approach to plane tilings, and in particular discusses Euler's theorem for tilings in generality (Chapter 3).