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SYMMETRY OF MATTER
Lesson 3 - Page 1

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Spirals are asymmetrical

Crystalline structures have their own descriptions to define symmetrical planes

LESSON 3.  Defining Symmetry

Geometry is the branch of mathematics dealing with the properties and relations of lines, angles, surfaces and solids.  All objects, whether the smallest protozoa to the largest building in the world, can be described through geometric descriptions. They are either symmetrical or asymmetrical.  Plane symmetry is the ability to divide an object into parts, equal in size and shape (congruent) and similar in position on either side of a dividing line or around a center. Transformation symmetry refers to the resulting symmetry after reflective, rotational, or translation movement of an object or design. In math and science symmetry provides a precise way to describe an object. 

A pattern is an arrangement of shapes or colors in a symmetrical design with a repeatable quality.  A pattern usually has a "unit cell" that repeats itself. A design of these unit cells is referred to as a tessellation or tiling.  Even if one tree (unit cell) repeats itself in a row, it is a pattern.  A row of pegs can be a row of trees.  Patterns are all around us. 

Symmetry can refer to two dimensional as well as three dimensional objects.  Some objects can have one or more symmetries. Describing symmetry is difficult for 3 dimensional objects that are more complicated than the Platonic solids.  Crystallographers have developed specific rules to help describe all these planes of symmetry.   In nature symmetry is not always perfect, but the terms are still applicable.  Remember, math is a tool that helps describe nature.  Math is exact, but sometimes nature is not.  The following are basic terms to help describe an object.