Of the seven crystal systems, the isometric system possesses the highest symmetry. Referred to as cubic by chemical crystallographers, the unit cell is characterized by three equal axes orthogonal to one another, so that a = b = c and alpha = beta = gamma = 90^o.

Keep in mind that cell parameters do not define the crystal class, but are a consequence of the symmetry elements that define the system. In the cubic system there will always be at least one 2, 4, 2bar, or 4bar axis and one 3 or 3bar axis. The five crystal classes are:

• Hexoctahedral
• Gyroidal
• Hextetrahedral
• Diploidal
• Tetartoidal

The following Java applets will show some of the major forms for the Hexoctahedral Class (symmetry 4/m3bar2/m). By rotating the applets, you can examine and identify the symmetry elements and location in each form (use left mouse button to rotate the figure, right button to resize the figure).

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Rotate each of the above figures and you can easily locate the symmetry elements present.

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