The crystallographic axes are the imaginary lines that we can draw within the crystal lattice. These crystal axis than works as the coordinate system within the crystal. These are well defined lines for the crystals.
- A crystal may have three or more crystal axes, and the angle between them can also varies.
“On the basis of number of crystal axes and mutual relationship between them we define a crystal system“
| Crystal system | Crystal axes | Characteristic symmetry elements | No. of classes |
| Isometric or Cubic system | a1 = a2 = a3 a1 ^ a2 ^ a3 = 900 | 4 axes of III fold symmetry | 5 |
| Tetragonal system | a1 = a2 ≠ c a1 ^ a2 ^ c = 900 | unique IV fold axes symmetry or VII fold axis of inversion | 7 |
| Hexagonal system | a1 = a2 = a3 ≠ c a ^ c = 900 | hexagonal division (unique VI fold axis or inversion) trigonal division (unique III fold axis or inversion) | hexagonal division -7 trigonal division – 5 |
| Orthorhombic system | a ≠ b ≠ c a ^ b ^ c= 900 | 3 axis of II fold symmetry | 3 |
| Monoclinic system | a ≠ b ≠ c a ^ c ≠ 900, b ^ c = 900 | 1 axis of II fold symmetry | 3 |
| Triclinic system | a ≠ b ≠ c a ^ b ^ c ≠ 900 | no axis or plane of symmetry | 2 |
- Cubic system : There are three axes. All the axes are perpendicular to each other and interchangeable.
- Tetragonal system : There are three axes. The two horizontal axes are of equal length and can be interchanged. The vertical axis can be longer or shorter. All the axes are perpendicular to each other.
- Hexagonal system :
- Hexagonal division – horizontal axes are equal and are interchangeable. all horizontal axes are perpendicular to the vertical axes.
- Trigonal division –
- Orthorhombic system : There are three axes. all are of unequal length but are mutually perpendicular to each other.
- Monoclinic system : There are three axes. all are of unequal length. a-axis is not perpendicular to vertical . b-axis is perpendicular to the c axis.
- Triclinic system :There are three axes. all are of unequal length. none of them are perpendicular to each other.
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