POLYPARALLELOGRAM PUZZLES AND TILING PROBLEMS (Raymond R. Fletcher Ill)

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A mathematical puzzle book which involves labeling vertices of a plane graph with elements from an abelian group G such that the labels applied to the bounding vertices of each region have the same sum in G. The plane graphs are those formed by the edges and vertices of various types of parallelograms fitted together edge to edge. We call these polyparallelograms. The polyparallelogram puzzles are organized into the following categories according to the types of parallelograms involved: (i) polysquares (or polyominoes; (ii) 60/120 rhombs; (iii) 36/144 and 72/108 rhombs (Penrose rhombs); (iv) various lattice parallelograms. The reader is introduced to the theory of polyparallelogram tilings of polygons, and challenged with problems and research questions at the end of each Chapter. All that is required of the elementary theory of graphs and abelian groups is included in the text. Also included are a variety of pure tiling problems involving nonparallelogram lattice quadrilaterals. “Polyparallelogram Puzzles and Tiling Problems” is a sequel to “Polycubes, Triangulations and Polyhexes over Zn” and features a similar type of puzzle but is more engaging mathematically.

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