The Collaborative International Dictionary of English v.0.48:

Symmetry \Sym"me*try\, n. [L. symmetria, Gr. ?; sy`n with,
   together + ? a measure: cf. F. sym['e]trie. See Syn-, and
   Meter rhythm.]
   1. A due proportion of the several parts of a body to each
      other; adaptation of the form or dimensions of the several
      parts of a thing to each other; the union and conformity
      of the members of a work to the whole.
      [1913 Webster]

   2. (Biol.) The law of likeness; similarity of structure;
      regularity in form and arrangement; orderly and similar
      distribution of parts, such that an animal may be divided
      into parts which are structurally symmetrical.
      [1913 Webster]

   Note: Bilateral symmetry, or two-sidedness, in vertebrates,
         etc., is that in which the body can be divided into
         symmetrical halves by a vertical plane passing through
         the middle; radial symmetry, as in echinoderms, is that
         in which the individual parts are arranged
         symmetrically around a central axis; serial symmetry,
         or zonal symmetry, as in earthworms, is that in which
         the segments or metameres of the body are disposed in a
         zonal manner one after the other in a longitudinal
         axis. This last is sometimes called metamerism.
         [1913 Webster]

   3. (Bot.)
      (a) Equality in the number of parts of the successive
          circles in a flower.
      (b) Likeness in the form and size of floral organs of the
          same kind; regularity.
          [1913 Webster]

   Axis of symmetry. (Geom.) See under Axis.

   Respective symmetry, that disposition of parts in which
      only the opposite sides are equal to each other.
      [1913 Webster]

WordNet (r) 3.0 (2006):

symmetry
    n 1: (mathematics) an attribute of a shape or relation; exact
         reflection of form on opposite sides of a dividing line or
         plane [syn: symmetry, symmetricalness,
         correspondence, balance] [ant: asymmetry,
         dissymmetry, imbalance]
    2: balance among the parts of something [syn: symmetry,
       proportion] [ant: disproportion]
    3: (physics) the property of being isotropic; having the same
       value when measured in different directions [syn: isotropy,
       symmetry] [ant: anisotropy]

Moby Thesaurus II by Grady Ward, 1.0:

106 Moby Thesaurus words for "symmetry":
   accord, accordance, affinity, agreement, arrangement, array,
   assent, balance, beauty, chorus, coequality, coextension,
   coherence, coincidence, communion, community, compatibility,
   concert, concinnity, concord, concordance, conformance,
   conformation, conformity, congeniality, congruence, congruency,
   congruity, congruousness, consistency, consonance, consort,
   cooperation, corelation, correlation, correlativism, correlativity,
   correspondence, deployment, disposal, disposition, equality,
   equation, equilibrium, equipoise, equipollence, equiponderance,
   equity, equivalence, equivalency, euphony, evenness, finish,
   formation, harmony, identity, intersection, inverse proportion,
   inverse ratio, inverse relationship, justice, layout, levelness,
   likeness, lineup, marshaling, measure, measuredness, mutuality,
   oneness, order, orderedness, orderliness, organization, overlap,
   par, parallelism, parity, peace, poise, proportion,
   proportionality, quiet, quietude, rapport, reciprocality,
   reciprocation, reciprocity, regularity, relativity, rhythm,
   routine, self-consistency, setup, structure, sweetness, sync,
   synchronism, system, tally, timing, tranquillity, uniformity,
   union, unison, unisonance