Tetragonal

The tetragonal system also has three axes that all meet at 90°. It differs from the isometric system in that the C axis is longer than the A and B axis which are the same length.

Trigonal

Again, the trigonal system is a subsystem of the hexagonal. Most gem references will list these as hexagonal.

Orthorhombic

In this system there are three axes, all of which meet at 90° to each other. However, all the axes are a different length.

Monoclinic

. The above crystal systems all have axes sides that meet at 90°. In the monoclinic system all the axes are different lengths. Two of them, the A and C axes, meet at 90°, but the third one does not.

Triclinic

In this system all the axes are different lengths and none of them meet at 90°.