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首页> 外文期刊>Crystallography reports >Gosset helicoids: I. 8D crystallographic lattice E-8 and crystallographic, quasi-crystallographic, and fractional helicoidal axes determined by this lattice
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Gosset helicoids: I. 8D crystallographic lattice E-8 and crystallographic, quasi-crystallographic, and fractional helicoidal axes determined by this lattice

机译：戈塞特螺旋线：I. 8D晶体学晶格E-8和由该晶格确定的晶体学，准晶体学和分数螺旋轴

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摘要

It is shown that mapping of substructures of a semiregular Gosset polytope, whose 240 vertices form the first coordination sphere of a 8D lattice E-8, determines the orders of p/d axes of helicoids that are set only by invariants of(sub)algebras. Axes of such (Gosset) helicoids are derived. These axes perform rotation by an angle (360 degrees/p)d; can be crystallographic. quasi -crystallographic (p = 2, 3, 4, 5, 6,...; d = 1), or fractional (I < d < p/2); and may belong to regular polytopes (conventional, starlike, etc.). Formation of ordered structures is considered as a formation of Gosset helicoids (rods) with their subsequent assembly. Helicoids with axes 15/4 and 15/7 are considered as examples. They correspond to crystal lographic approximants-helicoids with axes 4(1) and 2(1) composed of deformed icosahedra (dodecahedra)-in a beta-Mn crystal (clathrate IX).
机译：结果表明，半规形Gosset多面体的子结构的映射确定了仅由（sub）代数的不变量设置的螺旋体的p / d轴的阶数，该半球形多角形多面体的240个顶点形成8D晶格E-8的第一个协调球。 。派生此类（Gosset）螺旋线的轴。这些轴旋转角度为（360度/ p）d;可以结晶。准晶体学（p = 2，3，4，5，6，...; d = 1）或分数（I

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