In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate...

In crystallography, a crystallographic point group is a three-dimensional point group whose symmetry operations are compatible with a three-dimensional...

spectroscopy. Spectroscopic notation is based on symmetry considerations. The point group symmetry of a molecule is defined by the presence or absence of 5 types...

under a point reflection is said to possess point symmetry (also called inversion symmetry or central symmetry). A point group including a point reflection...

In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved. The unmoved points...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a...

The Elk Point Group is a stratigraphic unit of Early to Middle Devonian age in the Western Canada and Williston sedimentary basins. It underlies a large...

group (the images of a given point under all group elements) forms a discrete set. All finite symmetry groups are discrete. Discrete symmetry groups come...

The Six Point Group was a British feminist campaign group founded by Lady Rhondda in 1921 to press for changes in the law of the United Kingdom in six...

two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a...

Point Break were a British pop group, formed and managed by Danielle Barnett and signed to WEA, who found brief success between 1999 and 2000. Brett Adams...

geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere...

point group. This ranges from 1 in the case of space group P1 to 192 for a space group like Fm3m, the NaCl structure. The elements of the space group...

A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based...

rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups. This constraint means that the point group...

independent candidates in by-elections under the banner of the Nine Point Group. Following the electoral success of Tom Driberg with this support in...

crystallographic point group. A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned...

following possibilities (1D point groups): the symmetry group is the trivial group (no symmetry) the symmetry group is one of the groups each consisting of the...

isometries along the axis a discrete point group, frieze group, or wallpaper group in a plane, combined with any symmetry group in the perpendicular direction...

The Long Point Group is a geologic group in Newfoundland and Labrador. It preserves fossils dating back to the Ediacaran period. Earth sciences portal...

(wallpaper groups). Point group Crystallographic point group Space group Rod group Frieze group Wallpaper group Kopsky, V.; Litvin, D.B., eds. (2002). International...

the chiral polyhedral group, whereas the additional reflection symmetry is known as the full polyhedral group. One point group, pyritohedral symmetry...

Brillouin zone reduced by all of the symmetries in the point group of the lattice (point group of the crystal). The concept of a Brillouin zone was developed...

The groups each have a point group of the unit cell. In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier...

The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice...

The Connecting Point Group is a Late Neoproterozoic geological formation cropping out on the Avalon Peninsula of Newfoundland, dominated by deep marine...

the preimage of a point group (hence denoted 2G, for the point group G), or is an index 2 subgroup of the preimage of a point group which maps (isomorphically)...

Platonic solid not mapped to itself by point inversion. The regular tetrahedron has 24 isometries, forming the symmetry group known as full tetrahedral symmetry...

A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set...