Crystal Systems

There are six crystal systems:
1.Isometric
2.Hexagonal
3.Tetragonal
4.Orthorhombic
5.Monoclinic
6.Triclinic

 

Isometric Crystal System

How do you know it is isometric?
If a mineral belongs to the isometric crystal system, you will be able to find four 3-fold rotation axes on well-formed crystals of that mineral.
How do you know where the crystallographic axes are?
The isometric crystal system has three crystallographic axes that are mutually perpendicular to each other and are all the same length (a1, a2, and a3). These axes will coincide with the three 4-fold rotation axes (or the three 2-fold rotation axes if the particular sample lacks the 4-fold ones).
 
Hexagonal Crystal System

 

How do you know it is hexagonal?

If a mineral belongs to the hexagonal crystal system, you will be able to find only one 3-fold rotation axis OR only one six-fold rotation axis on well-formed crystals of that mineral.

 
How do you know where the crystallographic axes are?
The hexagonal crystal system has four crystallographic axes.  Three of them (a1, a2, and a3) are the same length, and they are at 120 degrees to each other.  The fourth axis (c) is of a different length, and it is perpendicular to the other three.  The “c-axis” will coincide with the 3-fold or 6-fold rotation axis.You can pick the three a-axes to be however you want them, as long as they are perpendicular to the c-axis, and they are 120 degrees apart from each other.The a-axes should either “come out” of an edge between faces or the middle of a face.

 

Tetragonal Crystal System
 

How do you know it is tetragonal?

If a mineral belongs to the tetragonal crystal system, you will be able to find only one 4-fold rotation axis OR only one four-fold rotoinversionaxis on well-formed crystals of that mineral.
 

How do you know where the crystallographic axes are?

The tetragonal crystal system has three crystallographic axes.  Two of them (a1 and a2) are the same length, and they are at 90 degrees to each other.  The third axis (c) is of a different length, and it is perpendicular to the other two.  The “c-axis” will coincide with the 4-fold or 4-fold rotoinversion axis.    You can pick the two a-axes to be however you want them, as long as they are perpendicular to the c-axis, and they are 90 degrees apart from each other.The a-axes should either “come out” of an edge between faces or the middle of a face.
 

Orthorhombic Crystal System
 

How do you know it is orthorhombic?

If a mineral belongs to the orthorhombic crystal system, you will be able to find either three two-fold rotation axes (with or without mirrors perpendicular to them) OR only one 2-fold rotation axis that has two mutually perpendicular mirror planes parallel to it.
 

How do you know where the crystallographic axes are?

The orthorhombic crystal system has three crystallographic axes (a, b, and c).  They are all of different lengths, and they are at 90 degrees to each other.  The crystallographic axes will either coincide with the 2-fold rotation axes OR they will be perpendicular to the mirror planes.

 
Monoclinic Crystal System

 

How do you know it is monoclinic?

If a mineral belongs to the monoclinic crystal system, you will be able to find only one 2-fold rotation axis and/or only one mirror.
 

How do you know where the crystallographic axes are?

The monoclinic crystal system has three crystallographic axes (a, b, and c), all of different lengths.  The angle between the b-axis and the a-axis is 90 degrees, and so is the angle between the b-axis and the c-axis.  However, the angle between the a-axis and the c-axis is at an angle different from 90 degrees.  The b-axis will either coincide with the 2-fold rotation axis OR it will be perpendicular to the mirror plane.The other axes will be perpendicular to the b-axis.  They will often be parallel to edges of the crystal faces.
 

Triclinic Crystal System
 

How do you know it is triclinic?

If a mineral belongs to the triclinic crystal system, you will be able to find only an inversion or 1-fold rotation axis.

 
How do you know where the crystallographic axes are?

The triclinic crystal system has three crystallographic axes (a, b, and c), all of different lengths, and all at angles different than 90 degrees.  The axes are often parallel to edges between crystal faces.  The c-axis is the longest and the a-axis is the shortest.