# More Tessellations Coloring Book

Available from CreateSpace and Amazon.

From the Introduction:

More Tessellations implies that there are already some. There are. This is my third coloring book of tessellations. It follows A Tessellating Coloring Book, published in 2012 and extensively revised in early 2015, and The Tessellating Alphabet Coloring Book, also in 2012.

Tessellations or tilings are made from a shape that repeats in a pattern to cover the plane with no overlaps or gaps. Simple tessellations are all around us. They can be seen in honeycomb of a beehive, brick walls, and regular and repeating paving and floor tilings. However, more complex shapes can also tessellate. The Dutch artist M.C. Escher (1898-1972) was obsessed with dividing the plane into repeating patterns of real-world objects. Before him almost all tessellations were geometric and abstract. Escher opened the world to a much wider range of tessellation shapes.

I became interested in tessellations after I developed a maze construction kit that combined two of my interests at the time, typography and computer programming. To make visually interesting mazes I needed visually interesting patterns and I quickly realized that tessellations were an important source of those patterns. A Tessellating Coloring Book collected over 100 tessellation patterns that I had either developed or adapted from the designs of others. Since its publication I have developed enough more to fill another coloring book. Most were designed in a review of ways to classify tessellation patterns. That adventure is recorded in another book, Exploring Tessellations: A Journey through Heesch Types and Beyond. This book is a way of reusing the efforts from that book in another format.

One classification of tessellations was developed by German mathematician Heinrich Heesch (1906-1995). His system requires that throughout the pattern the base tile keep the same size and that it connect with neighbors in only one way. It also requires that all edges of the tile be shapeable, which eliminates reflection over an edge because reflection requires a straight line. He found there were 28 ways to form tessellations that fit these requirements. You will note a great many bird patterns in the pages that follow. Exploring Tessellations began with an attempt to see how many of those 28 ways could be illustrated with a recognizable bird standing on the back of another bird. (I found 17.) Another classification system is the isohedral classes of Branko Grünbaum and Geoffrey Shepard. Their system has 93 classes, some of which have straight, unshapeable sides and others that place restrictions on how edges are shaped.

Without the computer program Tesselmaniac by Kevin Lee this book would not have been possible. The last page of the book contains notes giving the the Heesch types and isohedral classes used on each page as well as the symmetry group (the topic of another coloring book, Exploring Symmetry). If you wish to explore these classifications further, they are explained in Exploring Tessellations: A Journey through Heesch Types and Beyond.

Tessellations have been the exclusive design element in five of my maze books. Tantalizing Tessellating Mazes and More Tessellating Mazes are both appropriate for children as is Tessellating Alphabet Mazes for Kids. Both Puzzling Typography and Puzzling Typography A Sequel are aimed at an adult audience as are A Cornucopia of Mazes and Holiday Mazes, which have a mix of tessellating patterns and non-tessellating patterns. I apologize in advance for errors that remain in the book.

Robert Schenk
October 2015