Cubic(Isometric) Crystal System

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Cubic Crystal System – Normal (Holohedral) Class

The cubic crystal system (also called the isometric system) is one of the most symmetrical systems in crystallography. It has three mutually perpendicular axes of equal length, meaning all crystallographic axes (a, b, c) are identical.

The normal class (also called the holohedral class or hexakisoctahedral class) is the most symmetrical class within the cubic system, with fourfold, threefold, and twofold rotational symmetry axes, mirror planes, a center of symmetry, and an inversion center.

Symmetry Elements of the Cubic Normal Class (Galena type)

The normal class of the cubic system exhibits the highest degree of symmetry, including:

  1. Rotational Axes:

    • 3 Fourfold axes (C₄) along the principal crystallographic axes (x, y, z).
    • 4 Threefold axes (C₃) along the body diagonals of the cube.
    • 6 Twofold axes (C₂) along the face diagonals of the cube.

  2. Mirror Planes (m):

    • 9 mirror planes are present.
    • 3 are perpendicular to the crystallographic axes (xy, yz, zx planes).
    • 6 are diagonal, bisecting the angles between the axes.
    • 3.Inversion Center / Center of Symmetry (i):
    • Each point on the crystal has an identical counterpart on the opposite side of the center.

Forms in the Normal Class of the Cubic System

The normal class (holohedral) of the cubic system contains several important crystal forms, which include the following:

1. Hexakisoctahedron {hkl}

  • The most complex and symmetrical form in the cubic system.
  • Has 48 triangular faces, formed by modifying an octahedron with additional planes.
  • Example: Some synthetic crystals and modified natural crystals.

2. Octahedron {111}

  • Composed of 8 equilateral triangular faces.
  • The most common natural form found in the cubic system.
  • Example: Diamond (C), Fluorite (CaF₂), Magnetite (Fe₃O₄).

3. Cube (Hexahedron) {100}

  • Composed of 6 square faces, each perpendicular to one of the crystallographic axes.
  • Example: Halite (NaCl), Galena (PbS), Pyrite (FeS₂).

4. Rhombic Dodecahedron {110}

  • Has 12 rhombic faces.
  • Commonly seen in garnets and some minerals.
  • Example: Garnet Group (Almandine, Pyrope, etc.), Sphalerite (ZnS).

5. Tetrahexahedron {h0l}

  • Has 24 trapezoidal faces.
  • Found in some modified mineral growths.
  • Example: Some metallic crystals in artificial growth conditions.

6. Trapezohedron {hhl}

  • Has 24 trapezoidal faces.
  • A less common modification of cubic crystals.

Examples of Minerals in the Cubic Normal Class (Galena type)

  1. Diamond (C) → Typically octahedral in form.
  2. Halite (NaCl) → Cubic in form, commonly seen as rock salt.
  3. Fluorite (CaF₂) → Octahedral in form.
  4. Pyrite (FeS₂) → Cubic and sometimes pyritohedral in form.
  5. Garnet Group (Almandine, Pyrope, etc.) → Rhombic dodecahedral form.
  6. Galena (PbS) → Cubic form.
  7. Sphalerite (ZnS) → Rhombic dodecahedral or tetrahedral forms.

Crystallographic Notation for the Normal Class (Holohedral Class) of the Cubic System

  • Miller Indices for Forms:

    • Cube (100), (010), (001)
    • Octahedron (111), (1̅11), (11̅1), (111̅), etc.
    • Dodecahedron (110), (1̅10), (101), (10̅1), etc.
    • Hexakisoctahedron (hkl), where h ≠ k ≠ l

  • Point Group: 4/m 3̅ 2/m (Oh)

  • Space Groups:

    • Fm3̅m (e.g., NaCl, pyrite, galena)
    • Fd3̅m (e.g., diamond, fluorite, magnetite)

Importance of the Normal Class in the Cubic System

  • High Symmetry: This class represents the highest symmetry in the cubic system.
  • Common in Nature: Many economically important minerals, including diamonds, salt, and metallic ores, crystallize in this class.
  • Industrial and Scientific Applications: Understanding these forms is crucial in mineralogy, crystallography, and materials science, especially for synthetic crystal growth.


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