Central configurations of nested regular tetrahedrons

In this paper, we study the necessary and sufficient conditions about nested regular tetrahedrons, and prove that some nests do not form central configurations, some can. The necessary and sufficient conditions of central configurations are the masses of the inner layer and outer layer must equal, respectively, and the ratios of masses and distances of inner and outer layer must satisfy an equation.  2005 Elsevier Inc. All rights reserved.