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首页> 外文期刊>Acta crystallographica.Section D. Biological crystallography >Hexagonal and trigonal sphere packings. IV.Trivariant lattice complexes of trigonal space groups
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Hexagonal and trigonal sphere packings. IV.Trivariant lattice complexes of trigonal space groups

机译：六角和三角形包装范围。IV.Trivariant晶格三角形空间的复合体组

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The 13 trivariant lattice complexes with trigonal symmetry are compatible with 218 types of homogeneous sphere packings, 7 types of interpenetrating sphere packings and one type of interpenetrating layers of spheres. Altogether, the lattice complexes with trigonal characteristic space group (with 0, 1, 2 or 3 degrees of freedom) give rise to 225 types of sphere packing 110 of these types are compatible exclusively with one of the 13 trivariant lattice complexes, 31 in addition with some of the invariant, univariant or bivariant lattice complexes, whereas 6 types occur solely in such a lattice complex. 65 types encompass special sphere packings that can also be generated with hexagonal symmetry [Sowa, Koch & Fischer (2003). Ada Cryst A59, 317-326; Sowa & Koch (2004). Ada Cryst A60,158-166; Sowa & Koch (2005). Ada Cryst A61,331-342]; cubic inherent symmetry occurs for certain sphere packings [Fischer (2004), Ada Cryst A60, 246-249] belonging to 13 types. The maximal inherent symmetry is trigonal for 147 of the 225 types. The sphere packings of 61 types can be subdivided into connected layer-like subunits, those of 86 types into connected rod-like subunits. Such subunits may be used to construct some kind of 'descriptive symbols' that reflect certain properties of the sphere packings. Interpenetrating sphere packings with cubic inherent symmetry belong to one of the 7 types. All interpenetrating sphere layers that belong to the only type occurring in the trigonal crystal system show hexagonal inherent symmetry. Some examples depict crystal structures that can be described by means of sphere packings.
机译：13个trivariant晶格与三角形的复合物对称是兼容218种均匀球体包装,7种穿插的包装和一种类型的范围渗透的领域。三角晶格复合物特征空间群(0,1,2或3自由度)产生225种球包装110这些类型是兼容的专门的13 trivariant晶格除了一些复合物,31岁不变,单变的或bivariant晶格复合物,而6只发生在这样一个类型晶格复杂。球也可以生成的包装a61,331 - 342);某些领域包装(菲舍尔(2004),艾达结晶室A60, 246 - 249]属于13个类型。最大147年固有的对称性是三角形的225年的类型。可以细分为连接层86类型的子单元,这些连接棒状的子单元。构建某种“描述性的符号”反映领域的某些属性包装。立方对称属于固有的一个7类型。属于只发生在三角形的类型水晶系统显示六角固有的对称性。一些例子可以描述晶体结构被描述的包装范围。

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