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Reflection symmetry

In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.

Not to be confused with Point reflection.

In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical.

with respect to a non-isometric (an oblique reflection in a line, plane, etc.)

affine involution

with respect to .

circle inversion

For more general types of reflection there are correspondingly more general types of reflection symmetry. For example:

Patterns in nature

symmetry

Point reflection

theory of Reflection groups in Euclidean space

Coxeter group

(different type of symmetry)

Rotational symmetry

Chirality

Stewart, Ian (2001). What Shape is a Snowflake? Magical Numbers in Nature. Weidenfeld & Nicolson.

Mapping with symmetry - source in Delphi

from Math Is Fun

Reflection Symmetry Examples