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  2. Bravais lattice - Wikipedia

    en.wikipedia.org/wiki/Bravais_lattice

    Similarly, all A- or B-centred lattices can be described either by a C- or P-centering. This reduces the number of combinations to 14 conventional Bravais lattices, shown in the table below. [6]: 744 Below each diagram is the Pearson symbol for that Bravais lattice.

  3. Crystal system - Wikipedia

    en.wikipedia.org/wiki/Crystal_system

    A lattice system is a set of Bravais lattices (an infinite infinite array of discrete points). Space groups (symmetry groups of a configuration in space) are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices.

  4. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of ⁠ 1 / 2 ⁠ of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of ⁠ 1 / 3 ⁠ of ...

  5. Space group - Wikipedia

    en.wikipedia.org/wiki/Space_group

    The translations form a normal abelian subgroup of rank 3, called the Bravais lattice (so named after French physicist Auguste Bravais). There are 14 possible types of Bravais lattice. The quotient of the space group by the Bravais lattice is a finite group which is one of the 32 possible point groups.

  6. Periodic table (crystal structure) - Wikipedia

    en.wikipedia.org/wiki/Periodic_table_(crystal...

    The following table gives the crystalline structure of the most thermodynamically stable form(s) for elements that are solid at standard temperature and pressure. Each element is shaded by a color representing its respective Bravais lattice , except that all orthorhombic lattices are grouped together.

  7. Pearson symbol - Wikipedia

    en.wikipedia.org/wiki/Pearson_symbol

    The letters A, B and C were formerly used instead of S. When the centred face cuts the X axis, the Bravais lattice is called A-centred. In analogy, when the centred face cuts the Y or Z axis, we have B- or C-centring respectively. [5] The fourteen possible Bravais lattices are identified by the first two letters: