stylistic:style_transfer, stylistic:tone
Reflectional symmetry

Reflectional symmetry, linear symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.

In one dimension, there is a point of symmetry about which reflection takes place; in two dimensions, there is an axis of symmetry (a.k.a., line of symmetry), and in three dimensions there is a plane of symmetry. An object or figure for which every point has a one-to-one mapping onto another, equidistant from and on opposite sides of a common plane is called mirror symmetric (for more, see mirror image).

The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror images of each other. For example. a square has four axes of symmetry, because there are four different ways to fold it and have the edges match each other. Another example would be that of a circle, which has infinitely many axes of symmetry passing through its center for the same reason.

If the letter T is reflected along a vertical axis, it appears the same. This is sometimes called vertical symmetry. Thus one can describe this phenomenon unambiguously by saying that "T has a vertical symmetry axis", or that "T has left-right symmetry".

The triangles with reflection symmetry are isosceles, the quadrilaterals with this symmetry are kites and isosceles trapezoids.

For each line or plane of reflection, the symmetry group is isomorphic with C (see point groups in three dimensions for more), one of the three types of order two (involutions), hence algebraically isomorphic to C. The fundamental domain is a half-plane or half-space.