Symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time.

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element.

In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons.

In mathematics, a Lie group /ˈliː/ is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.

A triskelion or triskele is a motif consisting of a triple spiral exhibiting rotational symmetry.

A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality).

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

In physics, Lorentz symmetry, named for Hendrik Lorentz, is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed.

In abstract algebra, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutation operations that can be performed on n distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself.

Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection).

A geometric object has symmetry if there is an "operation" or "transformation" (technically, an isometry or affine map) that maps the figure/object onto itself; i.

Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry.

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper subrepresentation closed under the action of .

A taijitu (Traditional Chinese: 太極圖; Simplified Chinese: 太极图; Pinyin: tàijítú; Wade-Giles: t'ai⁴chi²t'u²) is a symbol or diagram (图 tú) in Chinese philosophy representing Taiji (太极 tàijí "great pole" or "supreme ultimate") representing both its monist (wuji) and its dualist (yin and yang) aspects.

In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn ( n ≥ 2 ).

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation, with modifiers to indicate certain subgroups.

Spontaneous symmetry breaking, a vacuum Higgs field, and its associated fundamental particle the Higgs boson are quantum phenomena.