设△ABC的三边分别为a、b、c,面积为S,则 a~2+b~2+c~2≥4(3~(1/2)S)当且仅当a=b=c时等号成立,这就是著名的Weisenbock不等式。对此不等式,本文将其推广到三维空间中的四面体,六面体,八面体,十二面体和二十面体中去。定理1 若S_1,S_2,S_3,S_4,V分别表示四面体ABCD的四个面的面积和体积,则 Let ΔABC have three sides a, b, and c, and the area is S, then a~2+b~2+c~2≥4(3~(1/2)S) if and only if a=b= When c is established, this is the famous Weisenbock inequality. For this inequality, this paper extends it to tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron in three-dimensional space. Theorem 1. If S_1, S_2, S_3, S_4, V represent the area and volume of the four faces of the tetrahedral ABCD, then