Inspired by scoring configurations in two of the Authors game creations, this book develops a theory involving polygons tiled with rhombs and polygons tiled with equilateral triangles. The constructions are complex but the mathematics involved is elementary. This book should be especially suitable to anyone with an interest in mathematics including High School and College students. Each Chapter is concluded with exercises which test understanding and pose open questions. Also included are complete rule sets for the “Game of Rhombs” and for the “Game of Triangles”. These games have been thoroughly tested by the Author and his wife and can be easily constructed using Mat board, an exacto knife, a compass and a straightedge.