ROTATION OF THE PARALLEL AND STEREOGRAPHIC PROJECTIONS OF THE CUBE

Last Update 19/ 10/ 2005

in English/ in Esperanto/ in Portuguese

This application shows the stereographic projection of a cube together with its parallel projection in gold. Drag the mouse on the green square to see both projections rotate simultaneously around a binary axis. When the green square is dragged to reach point A the triad axis (or the improper triad axis) will be coincident with the North South (NS) axis.

During the rotation of the cube as explained above no face pole keeps stationary, quite different when it is rotated around a tetrad axis coincident with the NS axis. Compare with the tetrahedron, when it is rotated around a triad axis coincident with the NS axis one face pole will also remain stationary in its stereographic projection.

Exercises

1) What is the orientation of the binary axis used to rotate the cube in this application?

2) Cite other rotation axes that can be orientated coincident with the NS axis with this application.

3) If initially one rotation axis of the cube is coincident with the NS axis, find the angle to shift the cube around the binary axis to make another rotation axis coincident with the NS axis.

4) Cite the symmetry elements that are always promptly recognized on the presented stereographic projection and do not change its orientation during the rotation performed by this application.

5) What is the condition to have a stationary face when a polyhedron is rotated around a symmetry axis?
Please send your comments.

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 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
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold