Last Update 27/ 03/ 2001

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The interactive figure shows the improper symmetry element named three fold screw axis, with symbol 31. Each blue sphere represents an equivalent position related with the mentioned axis.

The rotation angle of the three fold screw axis like the three fold axis is 120°. It is possible to interact with this applet by a push and drag mouse action on the green square in the bottom of the figure, to change the visual angle of the set. The three line segments connecting the blue spheres to the long line representing the screw axis are 120° from each other and displaced 1/3 of the repetition parameter of the crystal unity to which the symmetry element belongs. The long line supporting the three line segments described above represents the31 axis. It causes systematic diffracted rays extinctions, for example the diffracted rays with Miller indices (0 0 1), (0 0 2), (0 0 4), (0 0 5), (0 0 7), (0 0 8), etc. can not be observed due to the extinction or destructive interference when the 31 axis is parallel to direction z, measured with parameter c of the unit cell.


1. Stout, G.H. and Jensen, L.H., X-ray Structure Determination, Macmillan, London, 1972.

2. Buerguer, M.J., X-ray Crystallography, John Wiley & Sons, New York, 1966.

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Table of subjects.
Chemistry Analytical Chromatography
Elemental organic analysis
Volumetric analysis, simulation
Crystallography 3 fold screw axis
4 fold inversion axis on tetrahedron
5 fold rotation axis absent in crystallography
Binary axis and reflection plane in stereographic projection
Bravais lattices
Conic sections under symmetry operators
Converting from spherical coordinates to stereographic projection
Crystal lattice and unit cell
Determination of unit cell
Elements of symmetry in action - animation
Elements of symmetry in action - cube game
Elements of symmetry in action - dodecahedron game
Elements of symmetry in action - icosahedron game
Elements of symmetry in action - octahedron game
Elements of symmetry in action - tetrahedron game
Ewald sphere and crystal measurements
Five classes in the cubic system
Five classes in the rhombohedral system
From tetrahedron to prism
Gnomonic projection
Improper symmetry axis
Miller indices
Miller indices - animation
Miller indices - cube game
Miller indices - octahedron game
Miller indices - rhombic dodecahedron game
Miller indices - tetrahedron game
Mirror plane
Mirror planes and Miller indices game - tetrahedron
Orientations of the cube
Plane symmetry groups
Question on point group
Rotation axis in octahedron and Werner compounds
Rotation axis on tetrahedron and organic molecules
Rotation of objects about an arbitrary axis
Rotation of the parallel and stereographic projections of the cube
Rotation of the stereographic and parallel projection of the cube III
Seven faces in stereographic projection
Seven classes in the hexagonal system
Seven classes in the tetragonal system
Six elements of symmetry in seven orientations
Spherical projection of the octahedron
Stereographic projection
Stereographic projection of six polyhedra in different orientations
Straight line equations and symmetry elements
Symmetry, 2 fold axis
Symmetry, 2, 3 and 6 fold axis in benzene
Symmetry, 3 fold axis in the cube
Symmetry, 4 fold axis in the cube
Symmetry, 4 fold axis in the unit cell of gold
Symmetry elements and Miller indices game
Symmetry elements and Miller indices game - octahedron
Symmetry in art and in crystallography
Three classes in the monoclinic system
Three classes in the orthorhombic system
Twin crystals
Two classes in the triclinic system
Unit cell in hexagonal net
General Butane conformations
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold