These lattice systems are a grouping of crystal structures according to the axial system used to describe their lattice. Each lattice system consists of a set of three axes in a particular geometric arrangement. There are seven lattice systems. They are similar to but not quite the same as the seven crystal systems and the six crystal families.
The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube, that is, it exhibits four threefold rotational axes oriented at 109.5° (the tetrahedral angle) with respect to each other. These threefold axes lie along the body diagonals of the cube. The other six lattice systems, are hexagonal, tetragonal, rhombohedral (often confused with the trigonal crystal system),orthorhombic, monoclinic and triclinic.
| The 7 lattice systems (From least to most symmetric) | The 14 Bravais Lattices | |||
| 1. triclinic (none) |  | |||
| 2. monoclinic (1 diad) | simple | base-centered | ||
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| 3. orthorhombic (3 perpendicular diads) | simple | base-centered | body-centered | face-centered |
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| 4. rhombohedral (1 triad) |  | |||
| 5. tetragonal (1 tetrad) | simple | body-centered | ||
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| 6. hexagonal (1 hexad) |  | |||
| 7. cubic (4 triads) | simple (SC) | body-centered (bcc) | face-centered (fcc) | |
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