中文摘要：

本文研究R3中一类（4＋4＋1）-体中心构型.利用中心构型等价类的性质及代数、分析方法,得到了该构型构成中心构型的充分和必要条件,证明了对任意给定的质量比这类中心构型存在的结论,解决了给定不同质量比范围该类中心构型是否唯一的问题,推广了文[16]的结论.

英文摘要：

This article studies a kind of conjugate nested configuration for （4＋4＋1）-body problem in R3. The configuration consists of two regular tetrahedrons with a mass at their common geometrical center. Using properties of equivalent class of central configurations and algebraic and analytic methods, we obtain the necessary and sufficient conditions of the central configurations for these configurations and prove that the central configuration class exists and solve the problem that the central configurations are unique or not for any given mass ratios t, l, which extends the results in [16].