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首页> 外文会议>Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A >The Mathematics of Zeolite-like Possible Carbon and Boron Nitride Allotropes
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The Mathematics of Zeolite-like Possible Carbon and Boron Nitride Allotropes

机译：类沸石可能的碳和氮化硼同素异形体的数学

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摘要

Structures for low-density zeolite-like possible carbon and boron nitride allotropes can be constructed from networks of trigonal (sp~2) carbon atoms containing hexagons, heptagons, and/or octagons. The most symmetrical such structures are obtained by leapfrog transformations of either the Dyck tessellation of 12 octagons or the Klein tessellation of 24 heptagons. The Dyck and Klein tessellations can be obtained by subjecting a cube to quadrupling (chamfering) and septupling (capra) transformations, respectively. Both the Dyck and Klein tessellations can be embedded into genus 3 infinite periodic minimal surfaces of negative curvature. The automorphism group, ~4O, of the Dyck tessellation is a solvable group of order 96, the structure of which relates to the dual of the Dyck tessellation as the regular tripartite graph K_(4,4,4). However, the automorphism group, ~7O, of the Klein tessellation is a simple group of order 168, which can be generated from the prime number 7 in a way analogous to the generation of the icosahedral rotation group I (≈ the alternating group A_5) from the prime number 5.
机译：可以由包含六边形，七边形和/或八边形的三角形（sp〜2）碳原子网络构成低密度沸石状可能的碳和氮化硼同素异形体的结构。这种最对称的结构是通过12个八边形的Dyck镶嵌或24个七边形的Klein镶嵌的跨越式转换获得的。通过分别对立方体进行四倍（倒角）和七倍（capra）变换，可以得到戴克和克莱因镶嵌图。 Dyck和Klein镶嵌都可以嵌入到3类负曲率的无限周期性最小曲面中。 Dyck细分的自同构群〜4O是一个可解的96阶基团，其结构与Dyck细分的对偶关系为规则的三方图K_（4,4,4）。但是，Klein细分的自同构组〜7O是168阶的简单组，它可以由素数7生成，类似于生成二十面体旋转组I（≈交替组A_5）从素数5开始

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