Hexagonal system


Crystallographic Axes

All the crystal forms of Hexagonal system can be referred to three horizontal axes of equal lengths and a vertical axis of longer length which intersect the plane formed by horizontal axes. The horizontal axes are interchangeable. They are denoted by a1, a2 and a3.The angle between these horizontal axes is 120°. The vertical axis is denoted by c.

Symmetry Classes - 

The symetry classes which belong to this system are :

Beryl Type or Dihexagonal-bipyramidal class

Calcite Type or Ditrigonal-scalenohedral class

Tourmaline Type or Ditrigonal-pyramidal class

Quartz Type or Trigonal Trapezohedral class

Beryl Type Class

This class takes it's name from the common mineral Beryl (PbS), which belongs to it.

Symmetry

The symmetry of this class can be deduced from the typical form cube.

Planes 7 - 4 Axial and  3 Diagonal.

Axes 7 - 6 of two fold and 1 of four fold.

A centre of symmetry is present.

Forms

1) Basal Pinacoid - It is an open form consisting of two horizoontal faces. The miller symbol is (0001).

2) Hexagonal Prism of the Second Order - It is also an open form consisting of six vertical faces. Each face cuts one horizontal axis at the unit distance and other two horizontal axes at double distance and is parallet to the vertical axis. The general Miller symbol is (1120)onterh two's a solid having twelve rhomb shaped faces. 

3) Hexagonal Prism of First Order - It is also an open form consisting of six vertical faces. Each face cuts two horizontal axis at equall  distance and is parallel to the third horizontal axis and the vertical axis. The general Miller symbol is (1010)onterh two's a solid having twelve rhomb shaped faces.

4) Dihexagonal Prism - Dihexagonal prism ia an open form. It has twelve faces, each parallel to the vertical axis and cuts the three hosizontal axes at different lengths. It's Miller symbol is (2130).

5) Hexagonal Bipyramid - This is a closed form and it has 12 faces. Each face cuts the vertical axis and all three horizontal axes, one at the unit distance and other two at the twice distance. It's general Miller symbol is (1121). It is analogous with the second order prism.

6) Hexagonal Bipyramid - This is a closed form and it has 12 faces. Each face cuts the vertical axis and two horizontal axes at equal distance and being parallel to the other horizontal axis. It's general Miller symbol is (1011). It is analogous with the first order prism.

7) Dihexagonal Bipyramid - It's a Thsi is a double 12 sided pyramid. Each face cuts the horizontal axes at unequall distance and also the vertical axis. It's Miller symbol is (2131).