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.