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On the question of symmetry classification of ordered tetrahedrally coordinated structures

机译：关于有序四面体配位结构的对称分类问题

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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), 12401, (408), and 15, 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 > ->{1240} -> < 408 > -> {5, 3, 3}. The possibilities of the developed approach are demonstrated by the example of constructing a rod with the screw axis 8(2) from cells of the polytope < 136 >; this rod can be transformed into a diamond substructure: a helicoid of diamond parallelohedra with the screw axis 4(1).
机译：将四面体配位的多面体（4D多面体）的子结构确定为“多面体” {136）和{408}，将其分为四个中心四面体的不相交的17个顶点聚合。结果表明，菱形结构的17顶点多面体和多面体（136），12401，（408）和15、3、3）的区别仅在于外部顶点三重轴的同步旋转角度以及每个结构的像元由两个最接近的不相交的17顶点多面体确定。提出以下序列，作为有序四面体协调结构对称分类的基础：菱形结构-> <136>-> {1240}-> <408>-> {5，3，3}。通过从多面体<136>的单元格构造一个螺杆轴为8（2）的棒的示例，可以证明所开发方法的可能性。该杆可以转换为菱形子结构：螺旋轴为4（1）的平行六面体菱形螺旋。

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