Meissner 多面体的稠密性
The density of Meissner polyhedra
AI总结：
本文研究三维 Meissner 多面体，证明其在 Hausdorff 拓扑下于常宽体空间中稠密，并以现代视角重新审视 Sallee 的结果，结合球多面体与常宽体构造的最新进展。
摘要：
我们考虑 $\mathbb{R}^3$ 中的 Meissner 多面体。这些是常宽体，其边界由球面和纺锤环面的片段组成。我们通过取全等球的适当交集来定义这些形状，并证明它们在 Hausdorff 拓扑下在常宽体空间中稠密。这一稠密性断言本质上已由 Sallee 证明。然而，我们提供了一个现代视角，考虑到在理解球多面体以及基于这些形状构造常宽体方面的最新进展。
英文摘要：
We consider Meissner polyhedra in $\mathbb{R}^3$. These are constant width bodies whose boundaries consist of pieces of spheres and spindle tori. We define these shapes by taking appropriate intersections of congruent balls and show that they are dense within the space of constant width bodies in the Hausdorff topology. This density assertion was essentially proved by Sallee. However, we offer a modern viewpoint taking into consideration the recent progress in understanding ball polyhedra and in constructing constant width bodies based on these shapes.
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。
