双曲柏拉图流形和增广纽结三价图的普查
A census of hyperbolic platonic manifolds and augmented knotted trivalent graphs
摘要：
我们称一个3-流形为柏拉图的，如果它可以分解成等距的柏拉图立体。推广较早出版的作者和其他人在这样做的情况下，双曲理想四面体，我们给普查的双曲柏拉图流形和所有的柏拉图镶嵌。对于八面体的情况下，我们还确定了哪些流形是一个增广打结三价图的补充，并给出相应的链接。一个（小版本的）柏拉图式人口普查和相关的改进算法已被纳入SnapPy。人口普查也采用里贾纳格式。在附录中，我们表明，一个理想的立方体镶嵌可以细分成一个理想的几何三角剖分。
英文摘要：
We call a 3-manifold Platonic if it can be decomposed into isometric Platonic solids. Generalizing an earlier publication by the author and others where this was done in case of the hyperbolic ideal tetrahedron, we give a census of hyperbolic Platonic manifolds and all of their Platonic tessellations. For the octahedral case, we also identify which manifolds are complements of an augmented knotted trivalent graph and give the corresponding link. A (small version of) the Platonic census and the related improved algorithms have been incorporated into SnapPy. The census also comes in Regina format. In the appendix, we show that an ideal cubical tessellation can be subdivided into an ideal geometric triangulation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
