中文摘要：

用组合极值方法导出了n维欧氏空间中关于原点对称的一个凸多胞形子类上一个新的仿射不变量（最近由Lutwak，Yang和Zhang引入）的解析表达式，并给出了其在凸多胞形Minkowski问题的一个应用．

英文摘要：

Using the technique of combination extremum,it was obtained that the analytic expression of the affineinvariant functional, by Lutwak, Yang and Zhang recently introduced, defined on a speciiic subclass of origin-symmetric convex polytopes in n-dimensional Euclidean space, and an application of it to Minkowski problem for origin-symmetric convex polytopes was given.