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It has been suggested that this article be split into Symmetry and group (mathematics).

The term Symmetry arises in a number of contexts, and has several, related meanings all concerned with balance, equality and equivalence.:[1]

  • It may refer to an object which has balanced proportions, and the beauty of form arising from those balanced proportions, notably a face, or an animal, e.g. a tiger, as in the poem by William Blake (1757–1827):
TIGER, tiger, burning bright In the forests of the night, What immortal hand or eye Could frame thy fearful symmetry?
  • It may refer to the property of being mathematically symmetrical, especially relating to a correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis; sometimes the term bilateral symmetry is used in this context.
  • It may refer to an isometric transformation or rigid body motion of a geometric figure, which determines a one-to-one mapping onto itself, and which preserves angles and distances. There are four such kinds of isomorphism:Rotations, Reflections, Translations and Glide-Reflections
  • It may also refer to the property of remaining invariant under certain changes (as of orientation in space, of the sign of the electric charge, of parity, or of the direction of time flow) -- used of physical phenomena and of equations describing them.


  1. Initial definitions from: