Abstract
Substructures of tetrahedrally coordinated polytopes (4D polyhedra) are determined as “polytopes” {136} and {408}, which are divided into nonintersecting 17-vertex aggregations of four centered tetrahedra. It is shown that 17-vertex polyhedra of the diamond structure and polytopes 〈136〉, {240}, 〈408〉, and {5, 3, 3} differ only by the angle of synchronous rotation of external vertex triads, and the cell of each structure is determined by the two nearest nonintersecting 17-vertex polyhedra. The following sequence is proposed as a basis for symmetry classification of ordered tetrahedrally coordinated structures: diamond structure 〈136〉 {240} → 〈408〉 → {5, 3, 3}. The possibilities of the developed approach are demonstrated by the example of constructing a rod with the screw axis 82 from cells of the polytope 〈136〉; this rod can be transformed into a diamond substructure: a helicoid of diamond parallelohedra with the screw axis 41.
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Original Russian Text © A.L. Talis, O.A. Belyaev, A.A. Reu, R.A. Talis, 2008, published in Kristallografiya, 2008, Vol. 53, No. 3, pp. 391–396.
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Talis, A.L., Belyaev, O.A., Reu, A.A. et al. On the question of symmetry classification of ordered tetrahedrally coordinated structures. Crystallogr. Rep. 53, 359–364 (2008). https://doi.org/10.1134/S1063774508030012
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DOI: https://doi.org/10.1134/S1063774508030012