单冕镶嵌的对称性
Symmetries of Monocoronal Tilings
摘要：
某些平铺的顶点的顶点冠是顶点连同相邻的瓦片。所有顶点冠全等的镶嵌称为单冠。我们提供了一个分类的monocoronal平铺在欧几里得平面，并得出一个列表的所有可能的对称群monocoronal平铺。特别地，任何关于直接同馀的单冠镶嵌都是晶体学的，而任何关于同馀的单冠镶嵌（允许反射）要么是晶体学的，要么具有一维平移群。进一步得到了高维欧几里得空间中单冠镶嵌的平移群维数的界。
英文摘要：
The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher dimensional Euclidean space are obtained.
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