Rotational symmetry

thumb|The swastika is a symbol with many styles and meanings and has been used in many cultures and religions around the world for millennia. thumb|The Cultural appropriation|appropriation of the swastika by the [[Nazi Party (1920–1945) is the most recognisable modern usage of the symbol in the Western world.]]

intrinsic form of angular momentum as a property of quantum particles

physical quantity defined as the rate of change of angular position whose direction is (if regarded as a vector) the axis of rotation

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.

idealization of a solid body in which deformation is neglected (distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it)

thumb|Animation of a half-turn ambigram of the word ambigram, with 180-degree rotational symmetry An ambigram is a calligraphic composition of glyphs (letters, numbers, symbols or other shapes) that can yield different meanings depending on the orientation of observation. Most ambigrams are visual palindromes that rely on some kind of symmetry, and they can often be interpreted as visual puns. Although the concept is older, the term "ambigram" was coined by Douglas Hofstadter in 1983–1984.

quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital, and is symbolized as ℓ

matrices important in quantum mechanics and the study of spin

[[File:Regular_hexagon_as_intersection_of_two_triangles.png|thumb|A regular hexagram, [[List_of_regular_polytopes_and_compounds#Two_dimensional_compounds|{6}[2{3}]{6}]], can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green).]]

congruent transformation of a geometric space that preserves at least one point

third in a set of four quantum numbers that distinguishes the orbitals available within a subshell and can be used to calculate the azimuthal component of the orientation of orbital in space

special function over the surface of a sphere

ancient Armenian national symbol and a symbol of the national identity of the Armenian people

vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star

quantum number parameterizing spin and angular momentum

symmetry (something looking the same) under rotation

right|thumb|Interlaced triquetra which is a trefoil knot The triquetra ( ; from the Latin adjective triquetrus "three-cornered") is a triangular figure composed of three interlaced arcs, or (equivalently) three overlapping vesicae piscis lens shapes. It is used as an ornamental design in architecture, and in medieval manuscript illumination (particularly in the Insular tradition). Its depiction as interlaced is common in Insular ornaments from about the 7th century. In this interpretation, the triquetra represents the topologically simplest possible knot. thumb|Comparison of associated Reuleau

quantum mechanical operator related to rotational symmetry

A borjgali () is a Georgian symbol of the sun and eternity. The Borjgali is often represented with seven rotating wings over the tree of life which can be used to create various shapes and variations and is considered one of the main symbols of Georgian culture.

In Chinese philosophy, a taijitu () is a symbol or diagram () representing taiji () in both its monist (wuji) and its dualist (yin and yang) forms. A taijitu in application provides a deductive and inductive theoretical model. Such a diagram was first introduced by Neo-Confucian philosopher Zhou Dunyi of the Song Dynasty in his Taijitu shuo ().

coefficients in angular momentum eigenstates of quantum systems

group of rotations in 3 dimensions

quantum state of a system with a spin of quantum number s =1, such that there are three allowed values of the spin component, ms = −1, 0, and +1

quantum number describing the total angular momentum of an atom

study of systems of undeformable bodies under applied forces and how they change with time

3D symmetry group

3D symmetry group

coefficients coupled with angular momentum

irreducible representation of the rotation group SO

excited state dynamic in chemistry and physics

sum of multiples of four 3j symbols

full icosahedral symmetry

traditional motif showing three hares sharing ears

mixed quantum state of a system with a spin of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2

thumb|upright|Gankyil Unicode symbol (U+0FCB), ࿋, as rendered in Jomolhari (typeface)|Jomolhari font.

coupling in quantum physics

function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations are applied to its argument

symbol used in quantum mechanics

thumb|A geometrical hexafoil

In physics and particularly in particle physics, a multiplet is the state space for 'internal' degrees of freedom of a particle; that is, degrees of freedom associated to a particle itself, as opposed to 'external' degrees of freedom such as the particle's position in space. Examples of such degrees of freedom are the spin state of a particle in quantum mechanics, or the color, isospin and hypercharge state of particles in the Standard Model of particle physics. Formally, we describe this state space by a vector space which carries the action of a group of continuous symmetries.