摘要
定义 在n维欧氏空间En中,设n维单形∑A的顶点为Ai（i=1,2…,n+1）,ZA的内切球和各侧面的切点设为Ai＇,则称以Ai＇为顶点的单形∑A＇为单形∑A的切点单形。 若从n维单形∑A（∑A＇）的n+1个顶点中任取m+1个顶点,则可组成μ=（）个子单形,这些m维单形的体积记为Vh（m）(Vh（m）[m=1,2,…,n;h=1,2,…,。若(Vh（m）2(Vh（m）2的λ次初等对称多项式记为Pλ、Pλ＇;Vh（m）、Vh（m）的λ次初等对称多项式记为Qλ、Qλ＇[λ=1,2,…,]。
Definition Let be the vertex of a simplex ΣA in n-dimen-sional Euclidean space E' and Ai' be the tangent points which the inscribed sphere of ΣA is tangent to the side face of ΣA , then the simplex with the tangent points as vertexes is called the tangent points simplex.If m+ 1 vertexes are taken from n+1 vertexes of an n-dimensional simplex ΣA (ΣA') arbitrarily, then sub simplexes may be formed which the volume of these n-dimensional simplexes is respectively. If the λ-degree elementary symmetrical polynomial of and the λdegree elementary symmetrical polynomial of , then we have the following theorem.Theorem The invariants of n-dimensional simplexΣA and its tangent points simplex which are Pλ, Pλ'and Qλ, Qλ' satisfy inequalities ( 1 )The two equalities in ( 1 ) and ( 2 ) hold if and only if ΣA is regular simplex.
