- Reflection symmetry
**Reflection symmetry**,**line symmetry**,**mirror symmetry**,**mirror-image symmetry**, or**bilateral symmetry**issymmetry with respect to reflection.In 2D there is an axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric (see

mirror image ). Also seepattern .The

**axis of symmetry**of a two-dimension al figure is a line such that, if aperpendicular 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: the two halves are each other's mirror image. Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match. A circle has infinitely many axes of symmetry, for the same reason.If the letter T is reflected along a vertical axis, it appears the same. Note that this is sometimes called horizontal symmetry, and sometimes vertical symmetry. One can better use an unambiguous formulation, e.g. "T has a vertical symmetry axis."

The

triangle s with this symmetry are isosceles. Thequadrilateral s with this symmetry are the kites and theisosceles trapezoid s.For each line or plane of reflection, the

symmetry group is isomorphic with "C_{s}" (seepoint groups in three dimensions ), one of the three types of order two (involution s), hence algebraically "C_{2}". Thefundamental domain is a half-plane or half-space.Bilateria (bilateral animals, including humans) are more or less symmetric with respect to the sagittal plane.In certain contexts there is rotational symmetry anyway. Then mirror-image symmetry is equivalent with inversion symmetry; in such contexts in modern physics the term P-symmetry is used for both (P stands for parity).

For more general types of reflection there are corresponding more general types of reflection symmetry. Examples:

*with respect to a non-isometricaffine involution (anoblique reflection in a line, plane, etc).

*with respect to circle inversion.**ee also***

Rotational symmetry

*Translational symmetry **References***cite book |title=Symmetry |last=Weyl |first=Hermann |authorlink=Hermann Weyl |coauthors= |date=1982 |origdate=1952 |publisher=Princeton University Press |location=Princeton |isbn=0-691-02374-3 |pages= |url= |ref=Weyl 1982

**External links*** [

*http://republika.pl/fraktal/mapping.html Mapping with symmetry - source in Delphi*]

* [*http://www.mathsisfun.com/geometry/symmetry-reflection.html Reflection Symmetry Examples*] fromMath Is Fun

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