多面体上的局部方向保持对称保持运算
Local Orientation-Preserving Symmetry Preserving Operations on Polyhedra
摘要：
统一的方法，其中包括阿基米德，开普勒，戈德堡，卡斯帕和Klug，考克斯特，和康威，并扩展到以前的形式化的概念，局部对称性保持（LSP）的操作，我们介绍了一个正式的定义，本地操作的平面图，保持方向保持对称性，但不一定是方向反转对称性。这些操作包括，例如，手性Goldberg和Conway操作以及所有LSP操作。我们证明了我们的定义的合理性，以及引入一个不变量，可以用来系统地构建所有这样的操作。我们还显示了充分条件的操作，以保持其适用的平面图的连通性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
