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[6]: 744 Below each diagram is the Pearson symbol for that Bravais lattice. Note: In the unit cell diagrams in the following table all the lattice points on the cell boundary (corners and faces) are shown; however, not all of these lattice points technically belong to the given unit cell.
A lattice system is a set of Bravais lattices (an 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.
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 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 ...
In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional crystallographic lattice. According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions.
Zn has 6 nearest neighbors in same plane: 6 in adjacent planes 14% farther away [18] Cd has 6 nearest neighbours in the same plane- 6 in adjacent planes 15% farther away [ 18 ] If the unit cell axial ratio is exactly 2 2 3 ≈ 1.633 {\textstyle 2{\sqrt {\frac {2}{3}}}\approx 1.633} the structure would be a mathematical hexagonal close packed ...
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The Bravais lattice of the space group is determined by the lattice system together with the initial letter of its name, which for the non-rhombohedral groups is P, I, F, A or C, standing for the principal, body centered, face centered, A-face centered or C-face centered lattices. There are seven rhombohedral space groups, with initial letter R.