Up: Colleen Robles
I produced derivations of these pages at the Geometry Center in the Summer of 1998 for Science U.

Symmetry In the Plane

Introduction: What do you mean "symmetry"?

The symmetry groups in the plane are also often referred to as the Wallpaper Symmetries because they "wallpaper" (or generate a covering of) the plane.

The Beginning: Isometries

In order to understand the wallpaper symmetries one must first consider the four isometries or "rigid motions" of the plane. They are translation, rotation, reflection and glide reflection.

The Symmetries

Each isometry is constructed as a composition of isometries. Beginning with the "right" tile, annimations illustrate how the symmetries wallpaper the infinite plane.

Fun and Games!

Create your own wallpaper patters with Kali! The Geometry Center's Kali allows you to interactively explore the 17 symmetries in the plane and create your own beautiful images with them.


David E. Joyce has an great webpage on the wallpaper symmetries.