No abstract available

[en] Basic group-theoretical properties of the icosahedral point groups are derived. Here are given the permutations of the vertices of an icosahedron under the action of the elements of the icosahedral point groups, the icosahedral point groups' multiplication tables, subgroups, sets of conjugate subgroups, centralizers and normalizers of arbitrary subsets and closet and double coset decompositions. (orig.)

No abstract available

[en] The form of physical-property tensors of rank, 0, 1 and 2 invariant under the 32 crystallographic point groups and their subgroups are tabulated. This constitutes the basis for the tensorial classification of domain pairs in ferroic crystals which is given via a group theoretical classification of the corresponding physical-property tensor pairs. We tabulate this classification of tensor pairs for all physical-property tensors of rank 0, 1 and 2, and domain point-group symmetry. (orig.)

[en] The coset and double coset decompositions of the 32 crystallographic point groups with respect to each of their subgroups are tabulated. (orig.)

[en] A method is established for determining the spatial distribution of layer and rod group symmetries in a crystal. This method is based on the use of the so-called scanning theorem and scanning groups-equitranslational subgroups of the space group of the crystal, each of them uniquely being defined by a chosen set of parallel planes or lines. Classifying directions of planes and lines into orbits under the action of the point group of the space group in question, one applies the scanning theorem only to a chosen representative from each orbit. In analogy with Wyckoff positions, planes and lines which transect a crystal are classified into orbits under the action of the crystal's space group; the layer and rod groups corresponding to each such orbit are conjugate subgroups of the space group. (Author) 9 refs