Symmetry

See also: Symmetry in biology

Examples of symmetry in shapes.

3-rotational symmetry

Symmetric arcades of a portico in the Great Mosque of Kairouan also called the Mosque of Uqba, in Tunisia.

Reflectional Symmetry is a property of certain geometrical objects that appears the same when mirrored or reflected along an axis. This axis has to cross the shape through the middle of that object dividing into equal halves.

In rotational symmetry, the object is identical when it is rotated by a certain amount.

The precise notions of symmetry have various measures and operational definitions. For example, symmetry may be observed

• with respect to the passage of time;
• as a spatial relationship;
• through transformations such as rotation;
• through other kinds of transformations;
• as an aspect of scientific models, language, music and even knowledge itself.

Asymmetry

Asymmetry is the absence of symmetry. It is best defined like that because symmetry is relatively rare, and all other objects are asymmetric.

Symmetry Media

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  A spherical symmetry group with octahedral symmetry. The yellow region shows the fundamental domain.

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  A fractal-like shape that has reflectional symmetry, rotational symmetry and self-similarity, three forms of symmetry. This shape is obtained by a finite subdivision rule.

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  The triskelion has 3-fold rotational symmetry.

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  Many animals are approximately mirror-symmetric, though internal organs are often arranged asymmetrically.

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  Seen from the side, the Taj Mahal has bilateral symmetry; from the top (in plan), it has fourfold symmetry.

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  Persian rug with rectangular symmetry

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  Kitchen kaleidoscope quilt block

Further reading

• Stewart, Ian (2007). Why beauty is truth: the history of symmetry. Basic Books. ISBN 9780465082360.