The 14 3D Bravais Lattices

crystal system

Cubic a = b = c, α = β = γ = 90°

lattice system

P

I

C

i

0

1

j

0

1

k

0

1

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.

Crystal systems are determined by the relative lengths of the basis vectors

a

,

b

,

c

and the angles

(α,β,γ)

between them [1].

It is possible to shift the cell by one unit along a basis vector by selecting the

i

,

j

,

k

values. When repeated, this can generate the entire lattice.