BINARY AXIS AND REFLECTION PLANE IN STEREOGRAPHIC PROJECTION

in English/ in Esperanto/ in French/ in Portuguese

Last Update 25/ 02/ 2001

Interaction with this page may clarify the symmetry operation due to reflection plane and two fold rotation axis (or binary axis).

Initially the figure shows a crystal face pole from the north hemisphere represented in two stereographic projection diagrams, both with same coordinates. The left side will be reserved for the operation of binary axis and the right side for the reflection plane. After a click on button a the result is due to a binary axis containing the north pole (N) and the south pole (S) of the sphere and due to a reflection plane containing N and S. The graphic and literal symmetry element symbols are in red.

After a click on button b a new case with the face pole in a new position is presented. A foresight can be tried for this case if the same symmetry elements in the former orientation will be applied respectively. The actual result can be observed after a click on button c.

A click on button d shows another case, when the face pole is over S. To see the result after operation with the same symmetry element in this case, click on e.

To turn to the initial figure, click on f.

Bibliography

1. Stout, G.H. and Jensen, L.H., X-ray Structure Determination, Macmillan, London, 1972.

2. 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