Indiana University Bloomington
IUMSC   Indiana University Molecular Structure Center

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 = 90o.

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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The Cube or Hexahedron {001} is composed of six perfect square faces that make angles of 90o to each other.

The Octahedron {111} consists of eight equilateral triangular faces, each of which is has a corner on each of the three axes of the cubic cell.

Crystals usually have several forms, and can look remarkably different, depending on how pronounced each form is. The applet to the left and following applets show the progression from Cube to Octahedron.

Compare the faces in the five figures to watch the progression of the square faces as the applet shows the transformation from cube to octahedron.

The remaining cube form is easily seen as small squares.

This applet shows only the slightest hint of the cube form is left.

The Dodecahedron {011} consists of twelve rhomb-shaped faces. By rotating the applet, you will be able to see the various symmetry elements.

A combination of Cube and Dodecahedron forms.

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

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