论文标题
顶点信仰的常规Polyhedra
Vertex-Faithful Regular Polyhedra
论文作者
论文摘要
我们研究了忠实地在其顶点作用的自动形态群体的抽象常规多面体，并表明每个非灯泡抽象的常规多面体覆盖了一个“顶点 - 信仰”的多面体，并具有相同数量的顶点。然后，我们使用此结果，并在Flat Polyhedra上进行较早的工作，以基于其顶点集的大小来研究抽象的常规Polyhedra。特别是，我们将所有常规的多面体分类为顶点的数量或两倍的素数。我们还构建了最小的常规多面体，并具有主要平方数的顶点。
We study the abstract regular polyhedra with automorphism groups that act faithfully on their vertices, and show that each non-flat abstract regular polyhedron covers a "vertex-faithful" polyhedron with the same number of vertices. We then use this result and earlier work on flat polyhedra to study abstract regular polyhedra based on the size of their vertex set. In particular, we classify all regular polyhedra where the number of vertices is prime or twice a prime. We also construct the smallest regular polyhedra with a prime squared number of vertices.
