关于正则单形的注记

Note on Regular Simplex

指出了正则单形的新性质,如棱长为a的n维正则单形Ωn的体积V有下述公式1()!2Vn ann=+,任何n维正则单形?n的所有顶点角之和1 12 21n i(1)arcsin(1)(1 1)nin n∑=+α=++?+n,任何n维正则单形的所有二面角之和1 1≤i<∑j≤n+βij=???n 2+1arccos1/n,并借助于矩阵理论对已有的性质给出直观性的证明。

：The regular simplex was summarized, which pointed out new characters of regularsimplex. For example, the volume＇s formula of n dimension regular simplex is V=√n＋1/n!（α/√2）n is length edge）;The vertex angles＇ sum of any n dimension regular simplex Ωn .is n＋1∑i=1αi=（n＋1）arcsin（1＋n）1/2（1＋1/n）n/2 ;The dihedral angle＇s sum of any n dimension regular simplex is ∑1≤i≤j≤n＋1βij=〔n＋12〕arccos1/n .At the same time, the existing characteristics were certificated by the theory on matrix.