论文标题
优化Rupert属性
Optimizing for the Rupert property
论文作者
论文摘要
如果可以在其中切一个孔并将相同的多面体穿过孔中，则多面体是rupert。众所周知，所有5种柏拉图固体，13种阿基赛马固体中的10个，13个加泰罗尼亚固体中的9个以及92个约翰逊固体中的82个均为Rupert。在这里，设计了一种非线性优化方法，该方法能够在几秒钟内验证先前已知的结果。它还用于表明另外2种加泰罗尼亚固体 - 四亚抗体和五角形的Icositetrahedron-和另外5个Johnson固体是Rupert。
A polyhedron is Rupert if it is possible to cut a hole in it and thread an identical polyhedron through the hole. It is known that all 5 Platonic solids, 10 of the 13 Archimedean solids, 9 of the 13 Catalan solids, and 82 of the 92 Johnson solids are Rupert. Here, a nonlinear optimization method is devised that is able to validate the previously known results in seconds. It is also used to show that 2 additional Catalan solids -- the triakis tetrahedron and the pentagonal icositetrahedron -- and 5 additional Johnson solids are Rupert.
