The hexagonal system, one of the principal categories of crystal systems, in which the components of crystals are located by reference to four axes; three of these axes are of equal length and set at 120° to one another and a fourth axis is perpendicular to the plane of the other three axes. If the atoms or atomic groups in the solid are represented by points and the points are connected by line segments, the resulting lattice will define the edges of an orderly stacking of blocks, or unit cells. The hexagonal unit cell is distinguished by the presence of a single line, called an axis of 6-fold symmetry, about which the cell can be rotated by either 60° or 120° without changing its appearance.

The common minerals that crystallize in the hexagonal system are beryl, apatite, quartz, calcite, dolomite, and tourmaline.

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### Crystallographic axes of Hexagonal System:

All the crystals in the hexagonal systems are referred to four axes. Of these three (a1, a2, and a3) are of equal length. They lie in the horizontal plane with an angle of 120**° **between the positive ends. The fourth axis is vertical and is either longer or shorter than the other axes.

### Classes of the Hexagonal System:

The hexagonal crystal system is classified into two symmetry classes, i.e. Beryle Type, and Calcite Type.

**(1). Beryle Class of Hexagonal Crystals **

**Symmetry Elements of the Beryle Type: **The symmetry elements of the Beryle type are as follows.

- Planes:
- There are seven planes in this class of hexagonal crystals
- Six planes are vertical
- One plane is horizontal

- Axes:
- This class of hexagonal crystals has total 7 axes
- There is 1 vertical axis of 6-fold symmetry
- Apart from a vertical axis, there are 6 horizontal axes of 2-fold symmetry
- A center of symmetry

**Forms of Beryle Type of Hexagonal Crystal Systems: **The typical forms of this class are as follows.

**Basal Pinacoid (0001):**This form is composed of two horizontal faces which are parallel to the plane of horizontal axes.**Prism of First Order (101’0):**This form has six vertical faces. Each face intersects two of the horizontal crystallographic axes equally and is parallel to the third.**Prism of Second Order (112’0):**This form has six vertical faces. Each face intersects two of the horizontal axes equally and the intermediate horizontal axis at one-half this distance.**Dihexagonal Prism (hki’o):**This form is composed of 12 vertical faces. Each face intersects all three horizontal axes at different lengths. A common dihexagonal prims is (213’0).**Dipyramid of First Order (hoh’l):**This form is composed of 12 isoceles triangular faces. Each face intersects two of the horizontal crystallographic axes equally, is parallel to the third and cuts the vertical axis. There are various dipyramid depending on the inclination of the faces to the c-axis. The symbol of the unit form is (101’1).**Dipyramid of Second-Order hh2h’l):**This form is composed of 12 isosceles triangular faces. Each face intersects two horizontal axes equally, the intermediate horizontal axis at one-half this distance and also intersects the vertical axis. A common dipyramid of second order is (112’2).**Dihexagonal Dipyramid (hki’l):**This form is composed of 24 triangular faces. Each face intersects all three horizontal axes at different lengths and also intersects the vertical axis. A common dihexagonal dipyramid is (213’1).

### (2). Calcite Class of Hexagonal Crystal System:

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

- Planes:
- There are total of three planes in calcite type of crystals

- Axes:
- There are total of four axes in this type of crystals
- There is 1 vertical axis of 3-fold symmetry
- There are 3 horizontal axes of 2-fold symmetry
- A center of Symmetery

**Forms of Calcite Type of Hexagonal System: **The typical forms in this class are rhombohedron and the scalenohedron.

**Rhombohedron form of Calcite Types of Hexagonal Crystal System:**There are two rhombohedrons; one is positive (hoh’l), and the second is negative (ohh’l). This form is composed of six rhombo-shaped faces, of which three forces at the top alternate with three faces at the bottom. Each face intersects two of the horizontal axes equally, is parallel to the third and also intersects the vertical axis. Various rhombohedrons are possible depending on the inclination of the faces to the c-axis. The unit form of the positive rhombohedron is (011’1).**Scalednohedron (hki’l):**There are two scalenohedrons: (i) Positive (hki’l), and negative (khi’l). this form is composed of 12 triangular faces. Each face has a scalene triangle. Each face intersects all the horizontal axes at different lengths and also meets the vertical axis. A common positive scalenohedron is (213’1), and its complimentary negative scalenohedron is (123’1).

The basal pinacoid, prims of first order, prism of second order, dihexagonal prism, and dipyramid of second order, which are present in the beryl type are also found in this class, but these have lower symmetry.

**Relevant 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
- Tetragonal Crystal System