一类由正四面体和正八面体组成的共轭套中心构型

A new case configuration in R3,the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed.If the configuration is a central configuration,then all masses of outside layer are equivalent,the masses of inside layer are also equivalent.At the same time the following relation between p(r=√3/3ρ is the radius ratio of the sizes)and mass ratio r=～m/m must be satisfied r=-m/m=ρ(ρ+3)(3+2ρ+ρ2)-3/2+ρ(-ρ+3)(3-2ρ+ρ2)-3/2-4.2-3/2ρ-2-4-1ρ-2/2(1+ρ)(3+2ρ+ρ2)-3/2+2(ρ-1)(3-2ρ+ρ2)-3/2-4(2√2)-3ρ,and for any mass ratio T,when mass ratio T is in the open interval(0,0.03871633950…),there exist three central configuration solutions(the initial configuration conditions who imply hamagraphic solutions)corresponding radius ratios are r1,r2,and r3,two of them in the interval(2.639300779…,+∞)and one is in the interval(0.7379549890…,1.490942703…).when mass ratio T is in the open interval(130.8164950…,+∞),in the same way there have three corresponding radius ratios,two of them in the interval(0,0.4211584789…)and one is in the interval(0.7379549890…,1.490942703…).When mass ratio T is in the open interval(0.03871633950…,130.8164950…),there has only one solution T in the interval (0.7379549890…,1.490942703…).

A New Kind of Conjugate-nested Central Configurations in Consisted of One Regular Tetrahedron and One Regular Octahedron