Crystallographic point group and Hexagonal crystal family

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Difference between Crystallographic point group and Hexagonal crystal family

Crystallographic point group vs. Hexagonal crystal family

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. In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 lattice systems (hexagonal and rhombohedral).

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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Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

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Crystal system

In crystallography, the terms crystal system, crystal family and lattice system each refer to one of several classes of space groups, lattices, point groups or crystals.

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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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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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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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Point group

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

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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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Space group

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

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