de Oliveira Montauban Moreira, Eon Jean Guillaume
Instituto de Ciências Exatas, Matemática Pura, Universidade Federal Rural do Rio de Janeiro, Rio de Janeiro, Brazil.
Acta Crystallogr A. 2011 May;67(Pt 3):240-51. doi: 10.1107/S0108767311006179. Epub 2011 Mar 25.
Non-crystallographic (NC) nets are defined as periodic nets whose automorphism groups are not isomorphic to any isometry group in Euclidean space. This work focuses on a simple class of NC nets, restricted to nets with non-abelian, freely acting local automorphism groups. A general method is presented to derive such NC nets from crystallographic nets and some non-trivial examples are explored. It is shown that the labelled quotient graph of these nets does not necessarily possess non-trivial automorphisms which exchange cycles having the same net voltage. However, barycentric representations of these nets systematically display vertex collisions.
非晶体学（NC）网络被定义为其自同构群与欧几里得空间中的任何等距群都不同构的周期网络。这项工作聚焦于一类简单的NC网络，限于具有非阿贝尔自由作用局部自同构群的网络。提出了一种从晶体学网络导出此类NC网络的通用方法，并探索了一些非平凡的例子。结果表明，这些网络的标记商图不一定具有交换具有相同网络电压的回路的非平凡自同构。然而，这些网络的重心表示系统地显示出顶点碰撞。
