正规Tiling的邻居系

Collection of Neighborhoods of Normal Tiling

该文借助Tiling的拓扑图和边邻居图,给出了正规Tiling中两个Tiles拥有相同的邻居系的一个充分必要条件,并利用此条件证明了正规Tiling中不可能存在三个不同的Tiles具有相同的邻居系,从而在一定程度上回答了Gr_(u|¨)nbaum的一个公开问题.

In this paper,by using the topological graphs and the edge-neighbor graphs of tiling,we give a sufficient and necessary condition of two tiles of normal tiling having a same collection of neighborhoods.And it is proved that there exist impossibly three tiles with a same collection of neighborhoods in every normal tiling via the condition.Therefore,an open problem of Griinbaum is solved in some sense.