The 14 3D Bravais Lattices
Contributed by D. Meliga and S. Z. Lavagnino, with additional contribution by G. Follo
Download the CDF file to view the simulation using the free Wolfram CDF player.
This Demonstration shows the characteristics of 3D Bravais lattices arranged according to seven crystal systems: cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral and hexagonal. Each crystal system can be further associated with between one and four lattices by adding to the primitive cell (click "P"): a point in the center of the cell volume (click "I"), a point at the center of each face (click "F") or a point just at the center of the base faces (click "C"). The points located at the center/faces are highlighted in blue; each point is also a vertex or center of the cell/face, therefore each point is equivalent to every other point.


The Bravais lattice theory establishes that crystal structures can be generated starting from a primitive cell and translating along integer multiples of its basis vectors, in all directions.


[1] M. de Graef and M. E. McHenry, Structure of Materials: An Introduction to Crystallography, Diffraction and Symmetry, Cambridge: Cambridge University Press, 2007.

[2] W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, New York: Pergamon Press, 1958.

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