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Seven. They are:

Cubic - all angles 90 degrees, all sides equal length

Trigonal - all angles 90 degrees, two sides equal and the third unequal

Orthorhombic - all angles 90 degrees, no sides equal

Hexagonal - two angles 90 degrees and one angle 120 degrees, two sides unequal and the third unequal

Trigonal - all angles equal but not 90, all sides equal

Monoclinic - two angles 90, one more than 90, and no sides equal

Triclinic - no angles equal, no sides equal

For a graphical representation of these, see http://en.wikipedia.org/wiki/Crystal_system#Classification_of_lattices

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