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the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.
the proper or due proportion of the parts of a body or whole to one another with regard to size and form; excellence of proportion.
beauty based on or characterized by such excellence of proportion.
mathematics.

a geometrical or other regularity that is possessed by a mathematical object and is characterized by the operations that leave the object invariant:
a circle has rotational symmetry and reflection symmetry.
a rotation or translation of a plane figure that leaves the figure unchanged although its position may be altered.

physics. a property of a physical system that is unaffected by certain mathematical transformations as, for example, the work done by gravity on an object, which is not affected by any change in the position from which the potential energy of the object is measured.
contemporary examples

at that point, with a loss of symmetry in the power provided by the engines, the airplane banks sharply and dives, into the water.
how flight 370 could have become a zombie clive irving march 18, 2014

but, he says, what ultimately makes a hat look good on a person is the symmetry of the crown of their head to their jaw line.
the harlem hat shop you have to visit justin jones october 23, 2014

in a nice bit of symmetry, 56% of democrats said that bush should be impeached in july of 2007, according to a rasmussen survey.
the absurd impeachment feedback loop john avlon july 27, 2014

indeed there was something almost dantean about the symmetry of the punishment he suffered—the arch-insider was forced outside.
how boris berezovsky made vladimir putin, and putin unmade berezovsky owen matthews march 23, 2013

as a novelist, experience, he argues, matters less than “ordering, symmetry, and imagination.”
martin amis’ s-xual revolution olivia cole may 9, 2010

historical examples

in the symmetry of the dividing cell the basis of that resemblance which we call heredity is contained’.
progress and history various

i do not think those top-gallant-sails have the symmetry of the canvas of a ship-of-war.
homeward bound james fenimore cooper

the -ssembly vigorously entered on the work of bringing order out of confusion, symmetry out of chaos.
sketches of reforms and reformers, of great britain and ireland henry b. stanton

lastly, variety: variety is never so conspicuous, as when it is united with symmetry.
modern painters volume i (of v) john ruskin

slightness becomes supplanted by comparative solidity, commonness by novelty, lowness and irregularity by symmetry and height.
the hand of ethelberta thomas hardy

noun (pl) -tries
similarity, correspondence, or balance among systems or parts of a system
(maths) an exact correspondence in position or form about a given point, line, or plane see symmetrical (sense 2)
beauty or harmony of form based on a proportionate arrangement of parts
(physics) the independence of a property with respect to direction; isotropy
n.

1560s, “relation of parts, proportion,” from latin symmetria, from greek symmetria “agreement in dimensions, due proportion, arrangement,” from symmetros “having a common measure, even, proportionate,” from syn- “together” (see syn-) + metron “meter” (see meter (n.2)). meaning “harmonic arrangement of parts” first recorded 1590s. symmetrophobia is from 1809, supposed to be evident in egyptian temples and j-panese art.

symmetry sym·me·try (sĭm’ĭ-trē)
n.
exact correspondence of form and const-tuent configuration on opposite sides of a dividing line or plane or about a center or an axis.
symmetry
(sĭm’ĭ-trē)

an exact matching of form and arrangement of parts on opposite sides of a boundary, such as a plane or line, or around a central point or axis.

physics see invariance.

in geometry, the equivalence, point for point, of a figure on opposite sides of a point, line, or plane.