Figures with the axes of symmetry drawn in.

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. Image File history File links Symmetry. ... Image File history File links Symmetry. ... The elaborate patterns on the wings of butterflies are one example of biological symmetry. ... Sphere symmetry group o. ... In erik, a reflection (also spelled reflexion) is a map that transforms an object into its mirror image. ...

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 (see mirror image). Also see pattern. Sphere symmetry group o. ... A mirror image is a mirror based duplicate of a single image. ... A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned...

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. Sphere symmetry group o. ... 2-dimensional renderings (ie. ... Fig. ...

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. A triangle. ... In geometry, a quadrilateral is a polygon with four sides or edges and four vertices or corners. ... A kite showing its equal sides and its inscribed circle. ... An isosceles trapezoid. ...

For each line or plane of reflection, the symmetry group is isomorphic with C_s (see point groups in three dimensions), one of the three types of order two (involutions), hence algebraically C₂. The fundamental domain is a half-plane or half-space. The symmetry group of an object (e. ... A discrete point group in 3D is a finite symmetry group in 3D that leaves the origin fixed. ... In mathematics, an involution is a function that is its own inverse, so that f(f(x)) = x for all x in the domain of f. ... In mathematics, given a lattice Γ in a Lie group G, a fundamental domain is a set D of representatives for the cosets G/Γ, that is also a well-behaved set topologically, in a sense that can be made precise in one of several ways. ...

Bilateria (bilateral animals, including humans) are more or less symmetric with respect to the sagittal plane. Illustration of the different types of symmetry of Life Forms On Earth. ... In sciences dealing with the anatomy of animals, precise anatomical terms of location are necessary for a variety of reasons. ...

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). In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ...

For more general types of reflection there are corresponding more general types of reflection symmetry. Examples: In erik, a reflection (also spelled reflexion) is a map that transforms an object into its mirror image. ...

• with respect to a non-isometric affine involution (an oblique reflection in a line, plane, etc).
• with respect to circle inversion

In Euclidean geometry, of special interest are involutions which are linear or affine transformations over the Euclidean space Rn. ... In Euclidean geometry, oblique reflections generalize ordinary reflections by not requiring that reflection be done using perpendiculars. ... In mathematics, inversive geometry is the geometry of circles and the set of transformations that map all circles into circles. ...

See also

• left and right

A right-handed Cartesian coordinate system, presenting the z (up) vector and y (forward) vector, the right is defined to be the positive x vector. ...

External links

• Mapping with symmetry - source in Delphi
• Reflection Symmetry Examples from Math Is Fun