Last Update 19/ 10/ 2005
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With a mouse click on a selected button on this application one of the
17 different stereographic
projections will be displayed.
The button rows are organized from top to bottom in increasing number
of faces for the five polihedra of Platon followed by the rhombic dodecahedron.
Each number on button indicates the respective symmetry axis coincident
with the North South (NS) axis at the particular selected polyhedron orientation.
On the top of the keyboard an improper
tetrad axis (four
bar) appears.
The five fold rotation axis does not belong to the study of crystallography, however it can be observed in polihedra and in isolated structures as ferrocene, Fe(C5H5)2. Crystals may grow with platonic polyhedra habit, see the selection presented in table 1.
Table 1. Selection of crystals with some of its properties.
| Name, formula | Habit | Crystal system, unit cell, space group |
| Tetrahedrite, 3Cu2S.Sb2S3 | tetrahedron faces | cubic, a0=10.38 A, I-43m |
| Fluorite, CaF2 | cube | cubic, a0=5.46 A, Fm3m |
| Gold, Au | octahedral | cubic, a0=4.08 A, Fm3m |
| Pyrite, FeS2 | cube, dodecahedron, icosahedron | cubic, a0=5.42 A, Pa3 |
Garnets, as almandine, with the formula 3FeO.Al2O3.3SiO2, may have rhombic dodecahedron habit, its crystal system is cubic with unit cell parameter a0=11.53 A and space group Ia3d.
Exercises
1) Define the symmetry axis that is conicident with the NS axis when the first button at left is pushed.
2) Find the other symmetry elements observed in each stereographic projection above and its orientation.
3) Write a table with the spherical coordinates of the face poles for the cube, draw the respective stereographic projection with the aid of the converter and compare with the stereographic projection in this page.
4) Write a comment on the habit and the unit cell of the examples above.
Bibliography
Selected powder diffraction data for minerals, Joint commitee on powder diffraction standards, Pennsylvania, 1974.
Please send your comments.
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