Symmetry

thumb|upright=1.25|Symmetry (left) and asymmetry (right) thumb|upright=0.8|A spherical symmetry group with [[octahedral symmetry. The yellow region shows the fundamental domain.]] thumb|upright=0.8|A fractal-like shape that has [[reflectional symmetry, rotational symmetry and self-similarity, three forms of symmetry. This shape is obtained by a finite subdivision rule.]]

algebraic set with an invertible, associative internal operation admitting a neutral element

property of binary operations, for which changing the order of the operands does not change the result

scientific law regarding conservation of a physical property

thumb|Neolithic triple-spiral symbol

thumb|330px|Triptych of the The Elevation of the Cross (Rubens)|Raising of the Cross, Rubens, 1610–11, Antwerp Cathedral A triptych ( ) is a work of art (usually a panel painting) that is divided into three sections, or three carved panels that are hinged together and can be folded shut or displayed open. It is therefore a type of polyptych, the term for all multi-panel works. The middle panel is typically the largest and flanked by two smaller related works, although there are triptychs of equal-sized panels. The form can also be used for pendant jewelry.

thumb|A sphere is isotropic

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.

class of space groups, lattices, point groups, or crystals

group that is also a smooth manifold with group operations that are smooth

thumb|upright=1.4|A Function composition|composition of two opposite isometries is a direct isometry. A reflection in a line is an opposite isometry, like (reflection w.r.t the center diagonal line) or (reflection w.r.t the right diagonal line) on the image. Translation is a direct isometry: a rigid motion.

physical law that differentiable symmetries correspond to conservation laws

recursive visual effect

physical phenomenon in which the vacuum expectation value of a field is not invariant under a symmetry of the action, so that a symmetry present at high temperatures is broken at low temperatures

function from a set having some geometric structure to itself or another such set

thumb|right|400px|An w:Automorphism|automorphism of the Klein four-group shown as a mapping between two Cayley graphs, a permutation in cycle notation, and a mapping between two Cayley tables.

physics theorem

operation of the elements of a group as transformations or automorphisms (mathematics)

mechanism in quantum field theory in which spontaneous symmetry breaking causes gauge bosons to acquire mass

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geometric symmetry in living beings

group of transformations under which the object is invariant

group of bijective automorphisms of a set, also called bijective group: the group of bijections on a set (the group of all its permutations), whose group operation is function composition

feature of a system that is preserved under some transformation

group of isometries of Minkowski spacetime

symmetry with respect to an axis, when a shape which does not change upon undergoing a rotation around its symmetry axis

symmetry group of a configuration in space

T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, T: t \mapsto -t.

mathematical operation on Euclidian spaces which reverses distances with respect to a given point

symmetry (something looking the same) under rotation

symmetry of chemical molecules

equivalence in relativistic physics of observation with respect to change of (inertial) reference frame

scalar field whose vacuum expectation value spontaneously breaks electroweak gauge symmetry

research program on the symmetries of geometry

In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal).

nonabelian generalization of electrodynamics, which can be used to describe electroweak and strong nuclear interactions

phenomenon applied in physics

quantum field theory enjoying conformal symmetry

theorem

thumb|200px|Resonance made visible with black seeds on a harpsichord soundboard thumb|right|200px|Cornstarch and water solution under the influence of sine wave vibration 200px|thumb|A demonstration of sand forming cymatic patterns on a metal plate. Cymatics (from ) is a subset of modal vibrational phenomena. The term was coined by Swiss physician Hans Jenny (1904–1972). Typically the surface of a plate, diaphragm, or membrane is vibrated, and regions of maximum and minimum displacement are made visible in a thin coating of particles, paste, or liquid. Different patterns emerge in the excitato

study of geometry focusing on groups of geometric transformations

effect or phenomenon that is not invariant under a presumed or approximate symmetry of a physical system

symmetry in mathematics

classification system for crystals

invariance with respect to addition of a constant vector to a coordinate system

features that do not change if length or energy scales are multiplied by a common factor

type of linear representation

geometrical property and transformation

notation to represent symmetry in point groups

symmetry-based invariance to continuous group action

extension to the Poincaré group

Symmetry principle

type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself

regular polygonal symmetries

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150px|thumb|right|Benzene is a centrosymmetric molecule having a center of symmetry at the center

symmetry breaking in physics

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Physics theorem for symmetries of action