Axial relationship:
Crystals belonging to isometric or cubic system are referred to three crystallographic axes, which are equal in length and are perpendicular to each other.
Since these are mutually interchangeable, they are all designated by letter ‘a’. However, to distinguish them from each other and for proper orientation, they are designated as a, a2 and a. In proper orientation an axis runs from front to back, positive on observer side and negative on the other side; a2 axis runs from right to left, positive on the right hand side and negative on left hand side and a3 axis is vertical, positive at the top and negative at the bottom.
Axes a, and a, lie in the horizontal plane and a3 is vertical and perpendicular to the plane containing the, and a2 axes. Since all the crystallographic axes are equal in length the axial ratio (a: b: c) in case of isometric system is equal to five classes are grouped under this system.
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These are hex octahedral, hex tetrahedral, diploidic, gyroidal and tetartoidal. The hex octahedral class is the normal class of isometric system as it shows maximum symmetry among all classes and also as galena type after the characteristic mineral galena that crystallizes in this class.
Symmetry elements:
Crystals belonging to this class are characterized by three axes of 4-fold symmetry, which are coincident with the crystallographic axes. There are four axes of 3-fold symmetry, which emerge in the middle of each of the octants formed by intersection of crystallographic axes.
In addition, there are six axes of 2-fold rotation, each of which bisects one of the angles between two crystallographic axes. There are nine mirror planes, three axial i.e. each contains two of the crystallographic axes and six diagonal each of which bisects the angle between a pair of the axial planes. Centre of symmetry is also present.
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Forms:
The forms occurring in this class are listed in Table 3.1. Table 3.1 Forms of normal class of isometric system