教学经验。XIV.关于四面体的多样性

Yuriy Voytehovskiy
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引用次数: 0

摘要

论文提出了属于 8 个点对称组的 25 种组合几何四面体的推导。其中有 3 种简单形式:立方体(-43m)、四方体(-42m)和菱形(222)四面体;5 种组合形式:三棱锥和单面体(3m)、2 个平面二面体(mm2,2 种)、2 个轴二面体(2,3 种)、平面二面体和 2 个单面体(m,5 种)、4 个单面体(1,11 种)。结果表明,具有对称性 23、-4 和 3(立方四面体点对称群的子群)的四面体是不可能存在的。建议在晶体学 "简单形式及其组合 "课程中考虑该示例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
From teaching experience. XIV. On the variety of tetrahedrons
The paper proposes the derivation of 25 combinatorial-geometric kinds of tetrahedrons belonging to 8 point symmetry groups. Among them are 3 simple forms: cubic (-43m), tetragonal (-42m) and rhombic (222) tetrahedrons; and 5 combinations: trigonal pyramid and monohedron (3m), 2 planar dihedrons (mm2, 2 kinds), 2 axial dihedrons (2, 3 kinds), planar dihedron and 2 monohedrons (m, 5 kinds), 4 monohedrons (1, 11 kinds). It is shown that tetrahedrons with symmetry 23, -4 and 3 — subgroups of the point symmetry group of the cubic tetrahedron — are impossible. The example is recommended for consideration in the course of crystallography on «simple forms and their combinations».
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