Mathematical Symmetry

Mathematical symmetry plays an important and pervasive role in nature and in human design. There are several different types of mathematical symmetry, including:

Translational symmetry - An object, such as a tessellation, possesses translational symmetry if it can be translated (moved) by some distance and remain unchanged. A tessellation or pattern with translational symmetry is repeating, like a wallpaper or fabric pattern.
Rotational symmetry - An object possesses rotational symmetry if it can be rotated through some angle and remain unchanged. Examples of objects with rotational symmetry include automobile wheels, flowers, and kaleidscope patterns.
Glide reflection symmetry - An object possesses glide reflection symmetry if it can be translated by some distance and mirrored about a line or plane and remain unchanged.
Mirror symmetry - This is a special case of glide reflection symmetry, where the glide distance is zero.
Self similarity - This is a type of symmetry that fractal objects possess. If one can zoom in on a portion of an object and see something that is similar to (looks like) a reduced version of another portion of the object, then that object possesses self similarity. This type of symmetry is wide spread in nature. Examples include the system of arteries in the human body and the coastline of a continent.