论文标题
解决康威（Conway）和盖伊（Guy）的一些问题的解决方案
A solution to some problems of Conway and Guy on monostable polyhedra
论文作者
论文摘要
如果凸多面体只能在其一个脸上静止，则称为单个凸。本文的目的是调查康威的三个问题，即单一可见的多面体，该问题首次出现在1969年的戈德堡和盖伊（M. Goldberg and R.K. Guy，Polyhedra的稳定性）（J.H. Conway和R.K. Guy），Siam Rev. 11（1969），1969年），78-82，78-82）。在本说明中，我们回答了其中两个问题，并对第三个问题做出了猜想。我们证明的主要工具是一般定理，它描述了凸多面体在静态平衡点方面的光滑凸体近似值。作为该定理的另一种应用，我们证明了仅一个稳定和一个不稳定点的凸多面体的存在。
A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding monostable polyhedra, which first appeared in a 1969 paper of Goldberg and Guy (M. Goldberg and R.K. Guy, Stability of polyhedra (J.H. Conway and R.K. Guy), SIAM Rev. 11 (1969), 78-82). In this note we answer two of these problems and make a conjecture about the third one. The main tool of our proof is a general theorem describing approximations of smooth convex bodies by convex polyhedra in terms of their static equilibrium points. As another application of this theorem, we prove the existence of a convex polyhedron with only one stable and one unstable point.
