# Tetragonal Crystal System

In our previous post, we discussed in detail the classes and forms of Cubic/ Isometric Crystal System, which is a very common type of crystal and includes hundreds of minerals in this system. This post is about the ”tetragonal crystal system”. The tetragonal crystal system is another important system. Zircon, Cassiterite, and Rutile are the most common minerals of the tetragonal crystal system.

### Crystallographic Axes of Tetragonal Crystal System:

All the crystals in the tetragonal system are referred to as three mutually perpendicular axes. The two horizontal axes (a1 and a2) are equal but the vertical axis is of different lengths.

### Classes of Tetragonal Crystal Systems:

”Zircon Type” is the normal symmetry class of the tetragonal system.

### Zircon Class of Crystals:

**Symmetry:** The symmetry elements of this class are as follows.

- Planes: 5 planes
- 1 horizontal plane
- 4 vertical planes

- Axes: 5 Axes
- 1 vertical crystallographic axis of 4-fold symmetry
- 4 horizontal axes (2 crystallographic and 2 diagonal) of 2-fold symmetry

- A center of Symmetry

**Forms of Zircon Class of Crystals: **The typical forms of this class are as under;

**Basal Pinacoid (001):**This form is composed of two horizontal faces, which are parallel to the plane of horizontal zxes.**Prism of First Order (110):**This form is composed of four rectangular vertical faces. Each face intersects the two horizontal crystallographic axes at equal lengths and lies parallel to the vertical axis.**Prism of Second Order (100):**This forms has four rectangular vertical faces. Each face intersects one horizontal crystallographic axis and is parallel to the other two.**Ditetragonal Prims (hko):**This form has eight rectangular vertical faces. Each face intersects the two horizontal crystallographic axes at unequal distances and is parallel to the vertical axis. The common ditetragonal prim is (210).**Dipyramid of First Order (hhl):**This form is composed of eight isosceles triangular faces. Each face intersects the two horizontal crystallographic axes at equal distances and the vertical axis at a different lenght. The unit dipyramid of first order is shown in the following figure. The other dipyramid of first order are (221), (331), etc.**Dipyramid of Second Order (hol):**This form is composed of eight isosceles triangular faces. Each face intersects one horizontal axis and the vertical axis, and is parallel to the remaining axis. The various dipyramids of second order are (101), (201), (301), (102), etc.**Ditetragonal Di-Pyramids (hkl):**This form has 16 triangular faces. Each fae intersects all the three crystallographic axes, the intercepts on the horizontal axes being unequal. A common ditetragonal dipyramid is (311).

**Related Posts:**

- Introduction to Crystallography
- Unit Cells of the Crystal Lattice
- Crystallographic Axes
- Interfacial Angle of Crystals
- Parameters of Crystal faces
- Crystallographic Notation
- Forms of Crystal faces
- Symmetry Elements of Crystals
- Six Types of Crystal Systems
- Cubic/ Isometric Crystal System