the quality or state of being asymmetric.

1645–55; < Greek asymmetría lack of proportion. See a-6, symmetry Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
asymmetry (æˈsɪmɪtrɪ, eɪ-)
lack or absence of symmetry in spatial arrangements or in mathematical or logical relations

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1650s, "want of symmetry or proportion," from Gk. asymmetria, from asymmetros, from a- "not" + symmetros "commensurable."
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

asymmetry a·sym·me·try (ā-sĭm'ĭ-trē)
Disproportion between two or more like parts; lack of symmetry.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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Example sentences
It fits with a large body of research showing emotional asymmetry in the brain,
  he said.
Neither one of us was comfortable with the asymmetry in our roles or the
  apparent gender reversal.
It may not need a universal asymmetry to explain the prevalence of matter.
The thing that fascinates me is the asymmetry of this process.
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