(Isometric; Regular; Octahedral; Tesseral).
In this system the three crystallographic axes of reference are all at
right angles to each other and are equal in length. They are parallel
to the edges of the cube, and in the different classes coincide either
with tetrad or dyad axes of symmetry. Five classes are included in
this system, in all of which there are, besides other elements of
symmetry, four triad axes.
In crystals of this system the angle between any two faces P and Q
with the indices (hkl) and (pqr) is given by the equation
hp + kq + lr
COS PQ = ----------------------------------------
[root] [(h^2 +k^2 +l^2) (p^2 +q^2 +r^2)].
The angles between faces with the same indices are thus the same in
all substances which crystallize in the cubic system: in other systems
the angles vary with the substance and are characteristic of it.