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.

中文翻译：

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多面体的局部方向保持对称性保持操作

将 Archimedes、Kepler、Goldberg、Caspar 和 Klug、Coxeter 和 Conway 等人的方法统一起来，并扩展先前局部对称保持 (lsp) 运算概念的形式化，我们引入了平面图上局部运算的正式定义：保留方向保持对称性，但不一定是方向反转对称性。该操作包括例如手性 Goldberg 和 Conway 操作以及所有 lsp 操作。我们证明了我们定义的合理性，并引入了一个不变量，可用于系统地构建所有此类操作。我们还展示了一个操作的充分条件，以保持应用它的平面图的连通性。