没有鲁珀特性的凸多面体
A convex polyhedron without Rupert's property
Jakob Steininger and Sergey Yurkevich
arXiv
2025年8月25日
如果一个三维凸体的副本可以通过该体内的直孔，则称其具有鲁珀特性。在这项工作中，我们构造了一个可证明不是鲁珀特的多面体，从而反驳了2017年的一个猜想。我们还发现了一个是鲁珀特但不是局部鲁珀特的多面体。
A three-dimensional convex body is said to have Rupert's property if its copy can be passed through a straight hole inside that body. In this work we construct a polyhedron which is provably not Rupert, thus we disprove a conjecture from 2017. We also find a polyhedron that is Rupert but not locally Rupert.