Last Update 02/ 11/ 2001
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Interaction in this environment will allow observation of the normal to the crystal faces producing the perspective presentation of the spherical projection and the stenographic projection in a convenient orientation.
Nile's Sternness (1638-1687) recognized in 1669 the constancy of the dihedral angles in crystals of a material grown at equal temperature and pressure. This property, known as Stoniness law, has been used for analytical purposes. It is a handy work to draw the contour of the crystal faces when there are many of them. On practice the dihedral angle is substituted by its complement to trace the normal to the faces from an origin point. In the initial figure on this application the normal to the octahedral faces drawn in perspective pass through the origin point arbitrarily chosen as the octahedral centre. The intersection of any of the mentioned normal with a spherical surface centralized on the origin point will be defined as face pole. The set of eight face poles obtained is named spherical projection of the octahedron. The orientation of the octahedron related with the north south axis of the sphere (signed by N an S) can be modified by a push and drag mouse action on the green rolling bar. When the octahedral is oriented with two vertices along the NS axis then the respective stereographic projection is shown on the application. After a click on button b, the colour of each point in the stereographic projection is equal to the colour of the respective normal used to generate the face pole. Thus the green normal produces the green face pole in stereographic projection. As shown after a click on c, the spherical projection depends only on the normal to each face. However the representation of the octahedral without the normals to the faces is unable to build the spherical projection and consequently will not generate the stereographic projection, as observed after a click on d. The initial figure can be restored after a click on a.
Bibliography
1. Woolfson, M.M., X-ray Crystallography, Cambridge University Press, London, 1970.
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