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List of finite spherical symmetry groups

Index List of finite spherical symmetry groups

Finite spherical symmetry groups are also called point groups in three dimensions. [1]

28 relations: Coxeter notation, Crystallographic point group, Crystallography, Cyclic group, Cyclic symmetry in three dimensions, Dihedral group, Dihedral symmetry in three dimensions, Fundamental domain, Harold Scott MacDonald Coxeter, Hermann–Mauguin notation, Icosahedral symmetry, Involution (mathematics), John Horton Conway, List of planar symmetry groups, Norman Johnson (mathematician), Octahedral symmetry, Orbifold notation, PDF, Point groups in three dimensions, Point groups in two dimensions, Point reflection, Polyhedral group, Quaternion, Reflection symmetry, Regular polyhedron, Schoenflies notation, Tetrahedral symmetry, Triangle group.

Coxeter notation

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 expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

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Crystallographic point group

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind.

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Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Cyclic symmetry in three dimensions

In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) does not change the object.

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Dihedral group

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

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Dihedral symmetry in three dimensions

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).

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Fundamental domain

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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Hermann–Mauguin notation

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

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Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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List of planar symmetry groups

This article summarizes the classes of discrete symmetry groups of the Euclidean plane.

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Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

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Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.

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PDF

The Portable Document Format (PDF) is a file format developed in the 1990s to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.

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Point groups in three dimensions

In 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 sphere.

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Point groups in two dimensions

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

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Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

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Polyhedral group

In geometry, the polyhedral group is any of the symmetry groups of the Platonic solids.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

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Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

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Schoenflies notation

The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe point groups.

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Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

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Triangle group

In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.

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Redirects here:

List of Spherical Symmetry Groups, List of point symmetry groups, List of spherical symmetry groups.

References

[1] https://en.wikipedia.org/wiki/List_of_finite_spherical_symmetry_groups

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