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not identical on both sides of a central line; unsymmetrical; lacking symmetry:
Most faces are asymmetric.
(of a logical or mathematical relation) holding true of members of a class in one order but not in the opposite order, as in the relation “being an ancestor of.”.
Chemistry.

having an unsymmetrical arrangement of atoms in a molecule.
noting a carbon atom bonded to four different atoms or groups.
(of a polymer) noting an atom or group that is within a polymer chain and is bonded to two different atoms or groups that are external to the chain.

Contemporary Examples

I will bring unconventional and asymmetrical warfare to those in LAPD uniform whether on or off duty.
Rogue L.A. Cop’s Facebook Manifesto: ‘You Will Now Live the Life of Prey’ The Daily Beast February 7, 2013

But on Thursday, she was spotted having lunch in Miami with a brand new chin-length, asymmetrical blonde bob.
“Punk: Chaos to Couture” Ends As Fifth Most Popular Metropolitan Museum of Art Costume Institute Exhibit; Hermès Unveils $12,900 Basketball The Fashion Beast Team August 15, 2013

The collection ended with a bright finale: a blush-colored pink silk dress with an asymmetrical hem billowed down the runway.
Fashion Week Day 7 Isabel Wilkinson February 16, 2010

But asymmetrical information is also a term of art in economics.
How Product Labeling Killed Some Truly Righteous Weed and Might Even Raise Your Hospital Bill Megan McArdle May 7, 2013

Our matching passion for Nabokov and our otherwise mostly mismatching styles shaped our asymmetrical friendship.
Remembering Dmitri Nabokov, the Novelist’s Son and Literary Executor Brian Boyd May 9, 2012

Historical Examples

About one-half of the measured examples had asymmetrical shoulders.
Handbook of Alabama Archaeology: Part I Point Types James W. Cambron

Shoulders are narrow, usually tapered, and may be asymmetrical.
Handbook of Alabama Archaeology: Part I Point Types James W. Cambron

In many species of owl the two ear-openings are asymmetrical and differ in shape and size.
Jungle Folk Douglas Dewar

I could not find any asymmetrical somites, judging from the elytrophores.
Journal of Entomology and Zoology: Volume 6, Number 4, December 1914 Various

Ventral tentacular cirrus of second somite of a thin or foliaceous and asymmetrical form.
Journal of Entomology and Zoology, Vol. 11. No. 1. Various

adjective
not symmetrical; lacking symmetry; misproportioned
(chem)

(of a molecule) having its atoms and radicals arranged unsymmetrically
(of a carbon atom) attached to four different atoms or radicals so that stereoisomerism results
involving chiral molecules: asymmetric synthesis

(electrical engineering) (of conductors) having different conductivities depending on the direction of current flow, as of diodes
(aeronautics) having unequal thrust, as caused by an inoperative engine in a twin-engined aircraft
(logic, maths) (of a relation) never holding between a pair of values x and y when it holds between y and x, as “…is the father of…” Compare symmetric (sense 1), antisymmetric, nonsymmetric
adj.

1680s; see asymmetry + -ical. Other forms that have served as an adjective based on asymmetry are asymmetral (1620s), asymmetrous (1660s), and asymmetric (1875); only the last seems to have any currency. Related: Asymmetrically.

asymmetrical a·sym·met·ri·cal (ā’sĭ-mět’rĭ-kəl) or a·sym·met·ric (-rĭk)
adj.
Abbr. a
Lacking symmetry between two or more like parts; not symmetrical.