含双对称体的正二十面体壳体的几何性质
On the geometry of regular icosahedral capsids containing disymmetrons
摘要：
二十面体病毒衣壳是由衣壳的有序排列组成的。有三种类型的对称子：双对称子、三对称子和五对称子，它们具有不同的形状，分别以二十面体的2重、3重和5重对称轴为中心。在2010年[Sinkovits & Baker]给出了一个分类的所有可能的方式建立一个二十面体结构完全从三角形和五对称，这需要三角数T是奇数。在本文中，我们将双对称，以获得一个几何分类的二十面体病毒形成的定期五，三，和双对称。对于每一类的解决方案，我们进一步提供了公式的大小和奇偶校验限制h，k和T数。我们还提出了几种方法，其中不变量可用于对给定的配置进行分类。
英文摘要：
Icosahedral virus capsids are composed of symmetrons, organized arrangements of capsomers. There are three types of symmetrons: disymmetrons, trisymmetrons, and pentasymmetrons, which have different shapes and are centered on the icosahedral 2-fold, 3-fold and 5-fold axes of symmetry, respectively. In 2010 [Sinkovits & Baker] gave a classification of all possible ways of building an icosahedral structure solely from trisymmetrons and pentasymmetrons, which requires the triangulation number T to be odd. In the present paper we incorporate disymmetrons to obtain a geometric classification of icosahedral viruses formed by regular penta-, tri-, and disymmetrons. For every class of solutions, we further provide formulas for symmetron sizes and parity restrictions on h, k, and T numbers. We also present several methods in which invariants may be used to classify a given configuration.
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