The animation in this page enables the study of the symmetry element named four-fold inversion axis. This is an example of improper axis, represented by the red symbol below. The operation is performed by 90^o rotation followed by inversion through a point on the axis. For didactic reasons the axis is operated on four blue spheres centred on the corners of a static tetrahedron in perspective. After four successive operations a new cycle is started.

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Table of subjects.

Presentation
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
		Extinctions
		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
		p2mm
		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
Density
Electrochemical cell
Ethane conformations
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold