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.

Theme table
 

Presentation