The lattice centerings are:
Not all combinations of the crystal systems and lattice centerings are needed to describe the possible lattices. There are in total 7 × 6 = 42 combinations, but it can be shown that several of these are in fact equivalent to each other. For example, the monoclinic I lattice can be described by a monoclinic C lattice by different choice of crystal axes. Similarly, all A- or B-centered 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.
|The 7 Crystal systems||The 14 Bravais lattices|
| cubic||P (pcc)||I (bcc)||F (fcc)|
The volume of the unit cell can be calculated by evaluating where , and are the lattice vectors. The volumes of the Bravais lattices are given below:
In two dimensions, there are five Bravais lattices. They are oblique, rectangular, centered rectangular, hexagonal, and square.
In four dimensions, there are 52 Bravais lattices. Of these, 21 are primitive and 31 are centered.
Publication No. WO/2010/018515 Published on Feb. 18, Assigned to Koninklijke Philips Electronics for Lens Distortion Measurement, Correction (Dutch Inventors)
Feb 19, 2010; GENEVA, Feb. 19 -- Bas Hulsken and Sjoerd Stallinga, both of Netherlands, have developed a measuring and correcting lens...