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  2. Bravais lattice - Wikipedia

    en.wikipedia.org/wiki/Bravais_lattice

    The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by

  3. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:

  4. Pearson symbol - Wikipedia

    en.wikipedia.org/wiki/Pearson_symbol

    The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure, and was originated by W. B. Pearson. [1] The symbol is made up of two letters followed by a number. For example: Diamond structure, cF8; Rutile structure, tP6; The two (italicised) letters specify the Bravais lattice. The lower-case ...

  5. Space group - Wikipedia

    en.wikipedia.org/wiki/Space_group

    The Hermann–Mauguin (or international) notation describes the lattice and some generators for the group. It has a shortened form called the international short symbol, which is the one most commonly used in crystallography, and usually consists of a set of four symbols. The first describes the centering of the Bravais lattice (P, A, C, I, R ...

  6. Magnetic space group - Wikipedia

    en.wikipedia.org/wiki/Magnetic_space_group

    The table shows the 36 black-white Bravais lattices, including the 14 traditional Bravais lattices, but excluding the 14 gray lattices which look identical to the traditional lattices. The lattice symbols are those used for the traditional Bravais lattices. The suffix in the symbol indicates the mode of centering by the black (antisymmetry ...

  7. Crystal system - Wikipedia

    en.wikipedia.org/wiki/Crystal_system

    A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family.

  8. Hexagonal crystal family - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_crystal_family

    In either case, there are 3 lattice points per unit cell in total and the lattice is non-primitive. The Bravais lattices in the hexagonal crystal family can also be described by rhombohedral axes. [4] The unit cell is a rhombohedron (which gives the name for the rhombohedral lattice). This is a unit cell with parameters a = b = c; α = β = γ ...

  9. List of planar symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_planar_symmetry_groups

    The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).