This book explores a class of geometric patterns called tessellations, a pattern made up of one or more shapes which completely cover a surface without any gaps or overlaps. Focus in on one of the more elementary types of tessellations and investigation of them through concepts basic to art, geometry, and design. The seven chapters look at which shapes will tessellate, why certain shapes tessellate and others do not, how many different tessellating patterns can be created using two or more regular polygons; considerations of symmetry, and what techniques can be used to generate these intricate designs. Step-by-step instructions and suggested activities are provided for student production of both copied and original tessellations. An appendix, "Algebraic Analysis of Regular Polygons Around a Point," a glossary, and a bibliography conclude the book. (MM)