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

181440. Point groups in two dimensions Point groups in three dimensions Point groups in four dimensions Crystallography Crystallographic point group Molecular...

two-dimensional point groups are important as a basis for the axial three-dimensional point groups, with the addition of reflections in the axial coordinate...

In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group...

Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry...

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

symmetry group of both regular icosahedron and regular dodecahedron and has the order of a hundred-twenty. Point groups in three dimensions may also allow...

mirror planes remain unchanged. Molecular symmetry Point group Space group Point groups in three dimensions Crystal system Authier, André (2015). "12. The...

Finite spherical symmetry groups are also called point groups in three dimensions. There are five fundamental symmetry classes which have triangular fundamental...

There are 230 space groups in three dimensions, given by a number index, and a full name in Hermann–Mauguin notation, and a short name (international...

In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry...

table Crystallographic point group Molecular geometry Point groups in three dimensions Symmetry of diatomic molecules Symmetry in quantum mechanics Woodward...

isometry group is a Lie group. Point group Point groups in two dimensions Point groups in three dimensions Fixed points of isometry groups in Euclidean...

symmetry Point groups in three dimensions Screw axis Space group Translational symmetry Rotational symmetry of Weingarten spheres in homogeneous three-manifolds...

group. Frieze groups are two-dimensional line groups, having repetition in only one direction. They are related to the more complex wallpaper groups,...

system Frieze group Isometry Lattice Point group Point groups in two dimensions Point groups in three dimensions Space group Symmetry group Translational...

Q8: the quaternion group of order 8, also Dic2 The notations Zn and Dihn have the advantage that point groups in three dimensions Cn and Dn do not have...

studied – see point groups in three dimensions, polyhedral groups, and list of spherical symmetry groups. In 2 dimensions, the finite groups are either cyclic...

space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified...

point groups in three dimensions contain inversion: Cnh and Dnh for even n S2n and Dnd for odd n Th, Oh, and Ih Closely related to inverse in a point is...

In geometry, there exist various rotation formalisms to express a rotation in three dimensions as a mathematical transformation. In physics, this concept...

of reflection, the symmetry group is isomorphic with Cs (see point groups in three dimensions for more), one of the three types of order two (involutions)...

maximal compact group, and thus these correspond exactly to the polyhedral groups, the point groups in three dimensions. Icosahedral groups of Möbius transformations...

group Th of pyritohedral symmetry also has 24 members and a subgroup of index 3 (this time it is a D2h prismatic symmetry group, see point groups in three...

In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the...

In precise topological terms, each point of the 3-sphere has a neighborhood which is homeomorphic to an open subset of 3-D space. In three dimensions...

point symmetries (or equivalently, symmetries on the sphere). They are among the crystallographic point groups of the cubic crystal system. Seen in stereographic...

Dihydrogen cation Symmetry in quantum mechanics Group (mathematics) Point groups in three dimensions Complete set of commuting observables Born-Oppenheimer...

translational symmetry, so there are no associated crystallographic point groups or space groups. Presentations corresponding to the above are: I : ⟨ s , t ∣...

In geometry, the polyhedral groups are the symmetry groups of the Platonic solids. There are three polyhedral groups: The tetrahedral group of order 12...