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

在 R3 的一种新盒子配置，结合巢由一个常规四面体和一常规八面体组成了是配置是的 discussed.If 一种中央配置，当时，外面的层的所有群众是相等的，里面的群众层也是 equivalent.At 一样的时间在 p 之间的下列关系( r=3/3 是尺寸的半径比率)并且集体比率 r=m/m 一定是满足的r=-m/m=( +3 )( 3+2+2 )为任何妈的 -3/2+(-+3)(3-2+2)-3/2-4.2-3/2-2-4-1-2/2(1+)(3+2+2)-3/2+2(-1)(3-2+2)-3/2-4(22)-3。

A new case configuration in R^3, 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 ρ（r =√3/3ρ is the radius ratio of the sizes） and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ（ρ＋3）（3＋2ρ＋ρ^2）^-3/2＋ρ（-ρ＋3）（3-2ρ＋ρ^2）^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2（1＋ρ）（3＋2ρ＋ρ^2）^-3/2＋2（ρ-1）（3-2ρ＋ρ^2）^-3/2-4（2√2）^-3ρ, and for any mass ratio τ, when mass ratio r 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 τ 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 τ is in the open interval （0.03871633950…, 130.8164950…）, there has only one solution r in the interval （0.7379549890…, 1.490942703… ）.