**The 14 3D Bravais Lattices**

Contributed by D. Meliga and S. Z. Lavagnino, with additional contribution by G. Follo

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.

**Details:**

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.

**References:**

[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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