Symmetry in the Space of Euler Angles

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Abstract
For the analysis and description of textures the orientation distribution function f(g) is used. Orientations g as points in “orientation space” are usually characterized by the Euler angles φ1, Θ, φ2. The symmetries of the function f(g) result from the symmetries of the crystal and those of the specimen.The symmetries in orientation space induced by both the point group symmetry of the crystal and of the specimen are analysed. Any combination of crystal and specimen symmetries yield a group of linear transformations in orientation space; this group corresponds to one of the 230 space groups.If the point group of the crystal or the point group of the specimen belong to the cubic system the resulting group of linear transformations does not contain all induced symmetries.Tables with the induced space groups are given for all combinations of crystal and specimen symmetries.

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