# Seven (7) Crystal Systems

Crystals are divided into seven major systems on the basis of:

• Possible combinations of the elements of symmetry.
• In terms of three or four imaginary lines of reference called the Crystallographic Axes, which pass through the centre of the crystal.
• Crystals are allocated to seven systems according to the number of these axes, their lengths and the angles between them.

There is a conventional notation for the lettering and order of the crystallographic axes.

• In general, the vertical axis is called the “c” axis,
• That running from right to left is the “b” axis,
• That running from front to back is the “a”‘ axis.
• If the horizontal axes are equal in length, they are referred to as a1 and a2 and the third (vertical) axis is the “c” axis. If all the three axes are equal in length, they are referred to as a1, a2 and a3 and are interchangeable (as in the cubic system).

Crystallographic axes are not the same as the axes of symmetry. For example: In the Hexagonal, Trigonal and Tetragonal systems, the vertical “c” crystallographic axis coincides with the axis of 6-fold, 3-fold and 4-fold symmetry respectively. In the Orthorhombic system all the three crystallographic axes coincide with the three axes of 2-fold symmetry.

The most characteristic crystallographic elements are used in the following description of the seven crystal systems.

Cubic System (Isometric System)
No. of Crystal Axes: 3
Length: a1 = a2 = a3
Angles: at 90°
Symmetry Elements: a Center, 9 Planes, 13 Axes (6 of 2-fold, 4 of 3-fold, 3 of 4-fold)
Common Forms: Cube, Octahedron, Do-Decahedron, Tetrahedron etc.
Examples: Diamond, Garnet, Spinel, Fluorite, Pyrite, Lazurite etc.

Trigonal System
No. of Crystal Axes: 4
Length: a1 = a2 = a3 ≠ c
Angles: at 60°, “c” at 90° to their plane
Symmetry Elements: a Center, 3 Planes, 4 Axes (1 of 3-fold, 3 of 2-fold)
Common Forms: Rhombohedron, Prism, Pyramids, Basal Pinacoid etc.
Examples: Calcite, Quartz, Corundum, Tourmaline etc.

Tetragonal System
No. of Crystal Axes: 3
Length: a1 = a2 ≠ c
Angles: at 90°
Symmetry Elements: a Center, 5 Planes, 5 Axes (1 of 4-fold, 4 of 2-fold)
Common Forms: Tetragonal Prism, Bipyramid, Basal Pinacoid etc.
Examples: Zircon, Idocrase, Rutile, Scapolite etc.

Hexagonal System
No. of Crystal Axes: 4
Length: a1 = a2 = a3 ≠ c
Angles: at 60°, “c” at 90° to their plane
Symmetry Elements: a Center, 7 Planes, 7 Axes (1 of 6-fold, 6 of 2-fold)
Common Forms: Hexagonal Prism, Pyramids, Basal Pinacoid etc.
Examples: Beryl, Apatite, Benitoite etc.

Orthorhombic System
No. of Crystal Axes: 3
Length: a ≠ b ≠ c
Angles: at 90°
Symmetry Elements: a Center, 3 Planes, 3 Axes (all of 2-fold, 3 of 2 fold)
Common Forms: Prism, Pyramids, Pinacoids, Dome etc.
Examples: Andalusite, Chrysoberyl, Iolite, Peridot, Topaz etc.

Monoclinic System
No. of Crystal Axes: 3
Length: a ≠ b ≠ c
Angles: “a” axis inclined to the plane containing “band c”, “b and c” at 90°
Symmetry Elements: a Center, 1 Planes, 1 Axes of 2-fold
Common Forms: Prism, Pinacoids, Dome etc.
Examples: Jade, Orthoclase Feldspar, Sphene, Spodumene etc.

Triclinic System
No. of Crystal Axes: 3
Length: a ≠ b ≠ c
Angles: All inclined
Symmetry Elements: a Center, No Planes, No Axes
Common Forms: Pinacoids, Pedio etc.
Examples: Plagioclase Feldspar, Microcline Feldspar, Kyanite, Turquoise etc.