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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. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry
The known elementary particles respect rotation and translation symmetry but do not respect mirror reflection symmetry (also called P-symmetry or parity). Of the four fundamental interactions — electromagnetism , the strong interaction , the weak interaction , and gravity —only the weak interaction breaks parity.
C i (equivalent to S 2) – inversion symmetry; C 2 – 2-fold rotational symmetry; C s (equivalent to C 1h and C 1v) – reflection symmetry, also called bilateral symmetry. Patterns on a cylindrical band illustrating the case n = 6 for each of the 7 infinite families of point groups. The symmetry group of each pattern is the indicated group.
The role of symmetry in grouping and figure/ground organization has been confirmed in many studies. For instance, detection of reflectional symmetry is faster when this is a property of a single object. [29] Studies of human perception and psychophysics have shown that detection of symmetry is fast, efficient and robust to perturbations.
In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space.The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group.
Note: Pyritohedral symmetry can be written as , separating the graph with gaps for clarity, with the generators {0,1,2} from the Coxeter group , producing pyritohedral generators {0,12}, a reflection and 3-fold rotation. And chiral tetrahedral symmetry can be written as or , [1 +,4,3 +] = [3,3] +, with generators {12,0120}.
Thus reflection is a reversal of the coordinate axis perpendicular to the mirror's surface. Although a plane mirror reverses an object only in the direction normal to the mirror surface, this turns the entire three-dimensional image seen in the mirror inside-out, so there is a perception of a left-right reversal.
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]