In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s ≤ k. A tiling {\cal T} is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of {\cal T} is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k-transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane.

中文翻译：

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k-等冠状镶嵌

在本文中，提出了一个框架，可以系统地推导平面边到边k-瓷砖的等冠状瓷砖-s-传递性瓷砖，s≤k。平铺 {\cal T} 是k- 等冠状如果其顶点冠状形成k轨道或k其对称群作用下的传递性类。顶点的顶点冠X{\cal T} 用来指代与X。这k-等冠状平铺包括顶点-k-传递平铺（k-等角）和k- 统一的瓷砖。在一个顶点——k-传递平铺，顶点形式k其对称群下的传递性类。如果该平铺由正多边形组成，那么它是k-制服。本文还介绍了欧几里得平面中等冠状平铺的分类。