STEREOGRAPHIC PROJECTION OF SIX POLYHEDRA IN DIFFERENT ORIENTATIONS

Last Update 19/ 10/ 2005

in English/ in Esperanto/ in Portuguese

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.

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