Bravais lattice (3D)

A three-dimensional Bravais lattice is obtained by replicating any of the five two-dimensional lattices and stacking the replicated lattices above one another. The space lattices formed have lattice points that are generated by a set of translation operations described by the three-dimensional position vector r = ua + vb + wc.

There are exactly fourteen types of three-dimensional Bravais lattices that are grouped into seven lattice systems:

Lattice system





Triclinic \bigstar
Monoclinic \bigstar \bigstar
Orthorhombic \bigstar \bigstar \bigstar \bigstar
Tetragonal \bigstar \bigstar
Rhombohedral \bigstar
Hexagonal \bigstar
Cubic \bigstar \bigstar \bigstar

The unit cells of these lattices form the building blocks of all crystalline solids. We shall derive them in the following sections.


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