Isometric, Hexagonal and Monoclinic system

Isometric system: 


All those crystals that can be referred to three crystallographic axes, which are essentially equal in length at right angles to each other, and mutually interchangeable, are said to belong to the isomeric or cubic system.

Axial diagram

Since all the three axes are equal and interchangeable these are represented by the letter a. In the study position however the axes may be designated as a1,a2 and a3 the last being vertical.


Five symmetry classes fall in the Isometric system by virtue of their country The normal class is known as galena type. It has got the following symmetry.

a) Axes of symmetry:

    13 in all

3 are axes of four-fold symmetry

4 are axes of three-fold symmetry

6 are axes two fold of symmetry

b) Planes of Symmetry: 9 in all

3 planes of symmetry are at right angles to each other and are termed the principal planes;

6 planes f symmetry are diagonal in position and bisect the angles between the principal


c) It has centre of symmetry.


Following are the forms that commonly develop in the crystals belonging to isometric system.

1. Cube: A form bounded by six similar square faces each of which is parallel to two of three crystallographic axes and meets the third axis.

2. Octahedron: A form bounded by eight similar faces each of the shape of an equilateral triangle each meeting the three crystallographic axes at equal distances.

3. Dodecahdraon: It is form with twelves similar faces each of which is parallel to one of the three crystallographic axes and meets the other two at equal distances.

4. Trisoctahedron: A form of twenty four faces; each face meeting two axes at unit length and to the third at greater that unity.

5.Trapezohedran: A forms of 24 faces each faces meeting one axes at unit length and to the other two at greater than unity.

6. Hexaoctahedran: 48 faces; each face meets the three axis at unequal distances.

7. Tetra hexahedron: 24 faces each face meeting one axes and meet other to at unequal distance which are simple multiple of each other.

Other classes:

Isometric system comprises five symmetry classes in all. Beside the normal class following three classes are also represented among the minerals.

1.Pyritohedral Class

a) Symmetry            : 7 axes of symmetry of which 3 are axial axes of two fold symmetry 4 are diagonal axes of two fold symmetry,3 planes of symmetry. A centre of symmetry.

b) Forms : Pyritohedran and Diploid are two typical forms of this symmetry class. Diploid is a closed form of twenty-four faces that typically occur in pairs.

2.Tetrahedral class

a) Symmetry        : 7 axes of symmetry, 6 planes of symmetry diagonal, no centre of symmetry.

b) Forms : Most typical form of this class is a four-sided solid in which each face is an equilateral triangle. It is termed tetrahedron. It has a general symbol.

Hexagonal system

All those crystals, which can be referred to four crystallographic axes of which

i.Three axes are horizontal, equal, interchangeable and intersecting each other at 1200 between the positive ends.

ii.The fourth axes are vertical and at right angles to the three horizontal axes are grouped under the hexagonal system.

Axial diagram

The horizontal axes all being equal are designated by the letter a(a1,a2,a3)and the vertical axis by the letter ‘c’ as usual.


Forms of hexagonal system differ in character from forms of all the other systems in that their parameters, indices and symbols are determined with respect to four crystallographic axes. Thus the general form expresses the relation of any hexagonal form.

1. Base: An open form of two faces in which each face meets the vertical axis only.

2. Prisms: A prism as defined earlier is an open form in which each face is essentially parallel to the vertical axis.

Following three types of prisms are met with in the hexagonal system.

a)     Prism of 1st order. An open form of six faces in which each face is parallel to one of the three horizontal axes besides the vertical axis. It cuts the two horizontal axes at unit length.

b)    Prism of 2nd order. An open form of six faces like prism of 1st order but in this case each face cuts all the three horizontal axes, two axes at equal length and to the third at greater length.

c)     Prism of 3rd order: It is also called a dihexagonal prism as it has double the number of faces compared to the six faces of prism of 1st order.

Monoclinic system

The monoclinic system includes all those forms that can be referred to three crystallographic axes which are essentially unequal in length and further that can be of these is always inclined.

Axial diagram

All the three axes are unequal, they are designated by the letters a, b and c. The c axis is always vertical. The inclined axis is a- axis. It is inclined towards the observer and is also referred as clino axis.

Normal class symmetry

There are three symmetry classes placed in monoclinic system. The symmetry of the normal class is as given below:

a) Axis of Symmetry : 1 axis of two fold symmetry only

b) Planes of symmetry : 1 plane of symmetry only. And a centre of symmetry. The plane of symmetry is that plane which contains the crystallographic axes a and c.


The common forms of this system are

1) Pinacoid

it is an open from of two faces, each face being parallel to the two axes and cutting the third at a unit length .Three pinacoids are distinguished in the monoclinic system.

2. Domes

A dome is also form of two faces, each face meeting the vertical axis and one of the other two axes. It is a parallel to the third axis. Two types of domes are recognized:



ii) Clinodome

3. Prisms

There are three types of prisms is there;

i)       Unit prism 

ii)   Orthoprism 

iii) Clinoprism

4. Pyramid

These are closed forms and in these each face meets all the three axes.

i)                   Unit pyramid

ii)                Orthopyrmaid

iii)              Clinopyramid