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