SEVEN CLASSES IN THE TETRAGONAL SYSTEM

Last Update 16/ 09/ 2003

in Esperanto/ In English/ in Portuguese

After a click on any button at the right side of the figure the selected cyclic symmetry operation will be activated on the current crystallographic face pole represented in the stereographic projection. Each of the buttons operates a two stage combined symmetry element named inversion axis. This symmetry element is also known as improper axis, the first stage is a rotation similar as in the rotation axis to obtain an intermediate construction point which is reflected through a center point in order to get the final point in this second stage. This process will be repeated on the last final point in order to obtain a new final point until the original position is reached at the end of the cycle. In this application each inversion axis is coinciding with the North-South axis of the sphere.

The first two buttons on the top of the figure perform the same as the inversion center and the mirror plane, respectively.

Inversion axis are point group symmetry elements, at least the central point will stay stationary, it is immune to the operation.

A click on the circle will clear the figure and select a new face pole.

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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
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 the parallel and stereographic projections of the cube
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
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold