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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.
However, not all of the combinations are unique; some of the combinations are equivalent while other combinations are not possible due to symmetry reasons. This reduces the number of unique lattices to the 14 Bravais lattices. The distribution of the 14 Bravais lattices into 7 lattice systems is given in the following table.
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 ...
The fourteen three-dimensional lattices, classified by lattice system, are shown above. The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the Bravais lattices.
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 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.
The 14 lattice types in 3D are called Bravais lattices. They are characterized by their space group . 3D patterns with translational symmetry of a particular type cannot have more, but may have less, symmetry than the lattice itself.
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.