CLASSIFICATION OF CRYSTALS 2 (The Cubic or Isometric system)

1)    The Cubic System:

Figure 30: The crystallographic axes of the cubic system

-         It has 3 crystallographic axes all of equal lengths that is a = b = c, labeled; a₁ a₂ a₃

-         Its axial angles are such that α = β = γ = 90^o

-         The unit form is a solid with six square faces (a cube)

-         The diagnostic feature for the system is 4ⁱⁱⁱ fold.

          The Cubic system has 15 classes with the holomorphic class being the Hexoctahedral class.

                   i.            The Cubic Holosymmetric or (Hexoctahedral) class or Galena type:

It is the holosymmetric class of the Cubic system possessing 23 elements;

-         A center of symmetry

-         13 axes of symmetry (4ⁱⁱⁱ, 3^iv and 6ⁱⁱ)

-         9 planes of symmetry (3 axial and 6 diagonal)

-         Examples of minerals under this class include: free metals such as gold, silver, copper, lead, platinum, iron, halite (NaCl), galena (PbS), fluorite (CaF₂), and spinels including magnetite (FeO₄)

a.     Didodecahedral Class or Diploidal class or Pyrite type:

-         A center of symmetry

-         3 planes of symmetry

-         7 axes of symmetry (4ⁱⁱⁱ, 3ⁱⁱ)

-         Examples of minerals under this class include; pyrite (FeS2) and many nitrates.

b.     Hexatetrahedral class or Tetrahedrite type:

-         No center of symmetry

-         6 planes of symmetry

-         7 axes of symmetry (4ⁱⁱⁱ and 3ⁱⁱ).

-         Examples of minerals under this class include; sphalerite or blende (ZnS) and phosphate.

c.      Pentagonal or icositetrahedral class:

-         No center of symmetry

-         No plane of symmetry

-         3 axes of symmetry (4ⁱⁱⁱ, 3^iv and 6ⁱⁱ)

d.     Tetrahedral Pentagonal Dodecahedral class:

-         No center of symmetry

-         No plane of symmetry

-         7 axes of symmetry (4ⁱⁱⁱ and 3^iv)

Forms in the Isometric System

1.     Cube:  It is a form with 6 square faces at 90^o angles to each other.  Each face intersects 1 crystallographic axis and is parallel to the other two.  Its form notation is 
{ 0 0 I }

2.     Octahedron: It is a form composed of 8 equilateral triangles.  These triangle – shaped faces intersect all 3 crystallographic axes at equal lengths (the same distance from the origin).  Its form notation is { I I I }.  

3.     Dodecahedron (Rhombic Dodecahedron):  It is a form composed of 12 rhomb – shaped faces each of which intersects 2 crystallographic axes and is parallel to the 3^rd axis.  Its form notation is {0 I I }.

4.     Tetrahexahedron: It comprises 24 isosceles triangular faces each of which intersects 2 crystallographic axes; 1 at unity, the other at a different length and is parallel to the third.

5.     Tetrahedron:  it comprises 4 equilateral triangular faces, each of which intersects all 3 crystallographic axes at equal lengths.