Kronecker覆盖，V-构造，单位距离图和等距点圆构型
Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations
摘要：
我们称一个3维多面体P是可容许的，如果它具有以下两个性质：（1）对于P的每个顶点，它的第一邻点的集合是共面的;（2）由第一邻点确定的所有平面是不同的。证明了由容许多胞形P通过V-构造得到的点-平面构形的Levi图是其1-骨架的Kronecker覆盖。我们研究了V-结构的组合性质，并将其用于单位距离图上，构造了新的等距点圆构型。特别是，我们提出了一个无穷级数的所有成员的子配置著名的Clifford配置。
英文摘要：
We call a polytope P of dimension 3 admissible if it has the following two properties: (1) for each vertex of P the set of its first-neighbours is coplanar; (2) all planes determined by the first-neighbours are distinct. It is shown that the Levi graph of a point-plane configuration obtained by V-construction from an admissible polytope P is the Kronecker cover of its 1-skeleton. We investigate the combinatorial nature of the V-construction and use it on unit-distance graphs to construct novel isometric point-circle configurations. In particular, we present an infinite series whose all members are subconfigurations of the renowned Clifford configurations.
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