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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 symmetry group of a square belongs to the family of dihedral groups, D n (abstract group type Dih n), including as many reflections as rotations. The infinite rotational symmetry of the circle implies reflection symmetry as well, but formally the circle group S 1 is distinct from Dih(S 1) because the latter explicitly includes the reflections.
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.
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]
Letting τ ∈ G be the reflection of the arrowed edge, the composite figure X + = X # ∪ τX # has a bidirectional arrow on that edge, and its symmetry group is H = {1, τ}. This subgroup is not normal, since gX + may have the bi-arrow on a different edge, giving a different reflection symmetry group.
C nh, [n +,2], (n*) of order 2n - prismatic symmetry or ortho-n-gonal group (abstract group Z n × Dih 1); for n=1 this is denoted by C s (1*) and called reflection symmetry, also bilateral symmetry. It has reflection symmetry with respect to a plane perpendicular to the n-fold rotation axis. C nv, [n], (*nn) of order 2n - pyramidal symmetry or ...
Their symmetry group has two elements, the identity and the reflection in a line parallel to the sides of the squares. V and W also can be oriented in 4 ways by rotation. They have an axis of reflection symmetry at 45° to the gridlines. Their symmetry group has two elements, the identity and a diagonal reflection.
For a human observer, some symmetry types are more salient than others, in particular the most salient is a reflection with a vertical axis, like that present in the human face. Ernst Mach made this observation in his book "The analysis of sensations" (1897), [ 27 ] and this implies that perception of symmetry is not a general response to all ...