# Exploring Symmetry Coloring Book

Available from Amazon.

From the Introduction:

My interest in the technical details of symmetry came by the back door. After years of making mazes with symmetrical patterns, including many that were tessellations, I decided to learn what mathematicians had to say about tessellations. In the process of trying to make sense of tessellations, an effort that you can see in the book Exploring Tessellations: A Journey through Heesch Types And Beyond, I realized that I needed to know more about symmetry. I discovered that just as mathematicians had classified tessellations, they had classified symmetry patterns, finding that there are 17 two-dimensional symmetry groups. The discovery that all two-dimensional repeating patterns could be classified into just 17 groups was made by a Russian mathematician in the late 19th century and rediscovered by a Hungarian mathematician in the early 20th century. However, symmetry has been used since mankind began making decorative patterns. Examples for many or all of these groups can be found in the decorative work of people from around the world, including ancient Egypt, pre-Columbian America, and medieval Arabia. One does not need to know the mathematical details of symmetry to enjoy it or to create it.

The next six pages give a brief explanation of the 17 groups. In the remaining pages each group will be illustrated by at least two examples, most of which are patterns that I used in maze books. I have tried to limit use of well-known patterns and have avoided tessellations. (Tessellations are the subject of Exploring Tessellations: A Journey through Heesch Types And Beyond.) The format of a coloring book for this project offers an easy way to display patterns. Also, we live at a time when adults are enjoying coloring books of geometric patterns so a coloring-book format may appeal to a broad audience.

It is almost certain that mistakes remain in this text. I apologize in advance for those that I did not catch before publication.

October 2015