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The table below lists the 14 Bravis lattices within 6 crystal systems.
Six crystal systems: 

1. Triclinic: a1 ≠ b ≠ c, α ≠ β ≠ γ;
2. Monoclinic;
3. Orthorhombic;
4. Tetragonal;
5. Hexagonal;
6. Cubic;

 
The word "Symmetry" refers to a character of an object capable of repeating itself after a certain simple geometry operations. The operations include mirror, rotation, and inversion.
External symmetry was found on many natural minerals. Those minerals often have certain external symmetrical shape, such as angle relationship of surface.