STEREOGRAPHIC PROJECTION

Last Update 27/ 03/ 2001

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Interaction with this page may enhance the understanding on stereographic projection of a crystal face pole up from a projection on a sphere.

The stereographic projection is drawn on a two dimensional surface. Any face pole will be contained over a circumference or on its circle, according the respective spherical coordinates as can be observed on the right side of the figure. This circle is just the equatorial circle on the sphere.

On the left side of the figure a sphere in perspective projection can be observed, with the North pole and South pole signed by N and S, respectively. The blue curve represents the part of the sphere in front of the screen and the white curve the part behind the screen.

Points P and Q represent two crystal face poles projected on the sphere. A push and drag mouse action on the green square located in the centre of the figure will draw a line connecting points S and Q on the sphere. When this line intercepts the equatorial plane (drawn in perspective projection) a white point is drawn on the line and a little circle on the stereographic projection. On the other hand, a push and drag mouse action on the green square on the bottom of the figure will draw a line connecting points N and Q. In this case when this line intercepts the equatorial plane a white point is drawn on the line and a black point on the stereographic projection.

The equatorial plane drawn in perspective in the sphere is the stereographic projection drawn in perspective.

Any face pole on the equatorial circumference of the sphere is on the circumference of the stereographic projection, does not need to be projected.

Bibliography

1. Woolfson, M.M., X-ray Crystallography, Cambridge University Press, London, 1970.

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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
Mirror planes and Miller indices game - tetrahedron
Orientations of the cube
p2mm
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
Oxidation and reduction
Resources of chemical-ICT: water, health and symmetry
Solid and liquid gold