一次穿孔圆盘、非凸多边形和点面体
Once punctured disks, non-convex polygons, and pointihedra
摘要：
我们探讨了几个家庭的翻转图，所有相关的多边形或打孔多边形。特别是，我们考虑一次穿孔多边形的拓扑翻转图，反过来，包含所有可能的几何翻转图的多边形与一个标记点作为嵌入的子图。我们的主要重点是这些图的几何性质，以及它们如何相互关联。特别是，我们证明了它们之间的嵌入是强凸的（或者说，完全测地线）。我们还发现这些图的直径上的界限，有时使用强凸嵌入。最后，我们将展示这些图如何涉及到不同的多面体，即D型associahedra和一个家庭的二级多面体，我们称之为pointihedra。
英文摘要：
We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once-punctured polygons which, in turn, contain all possible geometric flip-graphs of polygons with a marked point as embedded sub-graphs. Our main focus is on the geometric properties of these graphs and how they relate to one another. In particular, we show that the embeddings between them are strongly convex (or, said otherwise, totally geodesic). We also find bounds on the diameters of these graphs, sometimes using the strongly convex embeddings. Finally, we show how these graphs relate to different polytopes, namely type D associahedra and a family of secondary polytopes which we call pointihedra.
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