Elementary knowledge

• Axis/ Rotational axis of Symmetry

  An imaginary line through a crystal around which it may be rotated and repeat itself in appearance one, two, three, four, or six times during a complete rotation
• Rotation axis types

  • 1-fold
  • 2-fold
  • 3-fold
  • 4-fold
  • 6-fold
• 1 fold Rotation axis


  • Requires rotation of a full 360° in order to restore to its original appearance
• 2 fold Rotation Axis


  • Requires a rotation of 180° to appear identical
• 3 Fold Rotation Axis


  • Object repeat itself every 120° rotation
• 4 fold rotation Axis


  • Object repeat itself every 90° rotation
• 6 fold Rotation Axis


  • Object repeat itself every 60° rotation
• Plane of Symmetry/ Mirror Plane


  An imaginary plane divides the crystal in two parts in such a way that one part is mirror of the other, the crystal is said to have a plane of symmetry
• Rotoinversion Axis


  A combination of rotation with a center of inversion
• Screw Axis


  Screw = Translation + Rotation. A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs
• Center of Symmetry/ Inversion Center


  An inversion center is a point within the crystal where every atom has an identical atom on the opposite side with the same distance but in the opposite direction
• Glide Plane


  A glide plane is a type of symmetry operation where a plane of symmetry is combined with a translation along a specific direction, this means when you apply the glide plane symmetry operation to a crystal structure, the structure is transformed in such a way that it appears identical to the original structure, but with a shift or translation along a particular direction
• Proper Axis/ Rotational axis of Symmetry

  -An imaginary line through a crystal around which it may be rotated and repeat itself in appearance one, two, three, four, or six times during a complete rotation.