AI 中文总结
研究锥化多面体框架的刚性阶数问题，引入瓦克斯普雷斯应力，利用其证明CPF是预应力稳定及二阶刚性的，通过将应力 - 挠曲猜想对偶公式与向量值施莱夫利型公式关联并给出新证明。
AI 中文摘要
锥化多面体框架（CPF）是通过在凸多面体的某个内点进行锥化从其一维骨架得到的杆 - 节点框架。最近表明CPF是刚性的，但其确切的刚性阶数仍未确定。本文引入了瓦克斯普雷斯应力并用它表明CPF是预应力稳定的，特别是二阶刚性的。为此，通过将其对偶公式识别为施伦克尔和苏阿姆引入的向量值施莱夫利型公式的推论，解决了瓦克斯普雷斯应力情况下的应力 - 挠曲猜想。我们给出了这个广义施莱夫利公式的一个新的纯离散几何证明。
英文摘要
A coned polytope framework (CPF) is the bar-joint framework obtained from the 1-skeleton of a convex polytope by coning over some interior point. It was recently shown that CPFs are rigid, though the exact order of rigidity remained open. In this paper we introduce the Wachspress stress and use it to show that CPFs are prestress stable, in particular, second-order rigid. To this end, we resolve the stress-flex conjecture in the case of the Wachspress stress by identifying its dual formulation as a corollary of a vector-valued Schläfli-type formula introduced by Schlenker and Souam. We give a new and purely discrete-geometric proof of this generalized Schläfli formula.
