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why there are only 14 bravais lattices not more or to be precise why trigonal structure doesnt ve bcc and fcc structure

why there are only 14 bravais lattices not more or to be precise why trigonal structure doesnt ve bcc and fcc structure

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Sakshi
askIITians Faculty 652 Points
8 years ago
In zero-dimensional and one-dimensional space, there is only one type of Bravais lattice.
In two-dimensional space, there are five Bravais lattices: oblique, rectangular, centered rectangular, hexagonal (rhombic), and square.
In three-dimensional space, there are 14 Bravais lattices. These are obtained by combining one of the seven lattice systems (or axial systems) with one of the seven lattice types (or lattice centerings).
Not all combinations of lattice systems and lattice types are needed to describe all of the possible lattices. It can be shown that several of the structures 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-centred lattices can be described either by a C- or P-centering. This reduces the number of combinations to 14 conventional Bravais lattices.

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