Reflection symmetry
Reflection symmetry, mirror symmetry, mirror-image symmetry, or
bilateral symmetry is
symmetry with respect to reflection.
It is the most common type of
symmetry. 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 .
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.
Encyclopedia
Reflection symmetry,
mirror symmetry,
mirror-image symmetry, or
bilateral symmetry is
symmetry with respect to reflection.
It is the most common type of
symmetry. 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 .
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: 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
triangles with this symmetry are isosceles, the
quadrilaterals with this symmetry are the
kites and the
isosceles trapezoids.
For each line or plane of reflection, the
symmetry group is isomorphic with
Cs , one of the three types of order two , hence algebraically
C2. The
fundamental domain is a half-plane or half-space.
Bilateria 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 .
For more general types of reflection there are corresponding more general types of reflection symmetry. Examples:
- with respect to a non-isometric affine involution .
- with respect to circle inversion
See also
External links
