14 Bravais Lattices
These files were created using Mathematica and LiveGraphics3D
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A Bravais lattice is the period arrangement of points that through repeated translation of the lattice vectors will fill space. Any lattice point can be reached from any other lattice point by a linear combination of integer multiples of the lattice vectors. The Bravais lattice will fill up space. In two dimensional space there are 5 possible Bravais lattices while in three-dimensional space there are 14 different Bravais lattices. In the models below, the 14 Bravais lattices are shown and can be rotated in space.
P - Primitive: simple unit cell
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Press the left mouse button and move the mouse to rotate the crystal lattices below.
Cubic Lattices.
a=b=c
α=β=γ=90°
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Tetragonal Lattices
a=b≠c
α=β=γ=90°
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Orthorhombic Lattices
a≠b≠c
α=β=γ=90°
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Monoclinic Lattices
a≠b≠c
α=β=90° γ≠90°
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Trigonal, Triclinic and Hexagonal Lattices
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a=b=c
α≠β≠γ≠90° |
a≠b≠c
α≠β≠γ≠90° |
a=b≠c
α=β=90° γ=60° |