等面单形的几何
The Geometry of an Equifacetal Simplex
摘要：
研究了余维各面全等的等面单形。它表明，等距群这样的单形的行为传递其顶点集，并作为一个应用，等面单形被证明有唯一的中心。证明了具有唯一中心的单形一定是等面的。引入并分析了等面单形组合型的概念，构造了偶数维等面单形的所有可能的组合型。
英文摘要：
Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its set of vertices, and, as an application, equifacetal simplices are shown to have unique centers. It is conjectured that a simplex with a unique center must be equifacetal. The notion of the combinatorial type of an equifacetal simplex is introduced and analyzed, and all possible combinatorial types of equifacetal simplices are constructed in even dimensions.
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。
