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symmetry

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Symmetry

A symmetry of an object is a transformation that can be applied to the object with the result that the object looks the same after the transformation as it did before.

The identity transformation is considered to be a symmetry of every object.

Rotational Symmetry

The rotational symmetries of an object are those symmetries which are rotations.

Reflectional Symmetry

The reflectional symmetries of an object are those symmetries which are reflections.

Symmetry Group

The symmetry group of an object consists of all of its symmetries. This includes the identity transformation.

Symmetries can be composed in that applying one symmetry and following it by another produces a transformation that is also a symmetry, namely that also has the effect of making the object look the same as it did originally. This makes the symmetries into a mathematical structure called a group.

category: definition

Revised on June 23, 2021 21:31:37 by Andrew Stacey
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