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]