论文标题
在Polyhedra上保存局部定向的对称性操作
Local Orientation-Preserving Symmetry Preserving Operations on Polyhedra
论文作者
论文摘要
统一的方法包括Archimedes，Kepler，Goldberg，Caspar和Klug，Coxeter和Conway，并扩展了先前对当地对称保存（LSP）操作的形式化的形式化，我们介绍了对当地操作的正式定义，这些定义在平面图上保存方向性化的对称性，但不一定是一定的。这些操作包括手性戈德堡和康威的操作以及所有LSP操作。我们证明了我们定义的健全性，并引入了一个不变的，该不变性可用于系统地构建所有此类操作。我们还显示了足够的条件，可以保留应用其应用的平面图的连接性。
Unifying approaches by amongst others Archimedes, Kepler, Goldberg, Caspar and Klug, Coxeter, and Conway, and extending on a previous formalisation of the concept of local symmetry preserving (lsp) operations, we introduce a formal definition of local operations on plane graphs that preserve orientation-preserving symmetries, but not necessarily orientation-reversing symmetries. This operations include, e.g., the chiral Goldberg and Conway operations as well as all lsp operations. We prove the soundness of our definition as well as introduce an invariant which can be used to systematically construct all such operations. We also show sufficient conditions for an operation to preserve the connectedness of the plane graph to which it is applied.
