TABLE OF CONTENTS Most people have a sense of what symmetry is and can easily recognize a symmetric object. The ability to identify symmetry in various situations is a useful skill that is used in many arts and professions. In science, symmetry goes beyond simple geometry and plays a major role in the understanding of many phenomena. We will use symmetry later in this book to understand liquid crystals and some of the molecules of life. This chapter will introduce some concepts of symmetry and answer the following questions:
What is symmetry? Why should we care?
What are the basic symmetry operations how does one repeat a pattern in a symmetric manner?
Can simple symmetry operations be combined into more complex symmetry patterns? How does one do this?
How does one develop the skills to observe and discern symmetry in objects?
You are familiar with some aspects of symmetry. For example, you know that, to a very good approximation, a mirror placed along a line extending from the middle of your nose through your navel will reveal that the left and right sides of your external body are symmetric. Similarly, you know that there is something symmetric about your left and right hands. Many of us admire the petals of flowers and their seemingly symmetric organization, and see a certain beauty in a well-built fence.
An understanding of symmetry will be of assistance in understanding solids and liquid crystals. In fact, one of the fundamental postulates of crystal physics is
