+87 Let \(A_1 A_2 A_3 A_4\) be a regular tetrahedron. Let \(P_1\) be the center of face \(A_2 A_3 A_4\) and define vertices \(P_2, P_3\) and \(P_4\) the same way. Find the ratio of the volume of tetrahedron \(A_1 A_2 A_3 A_4\) to the volume of tetrahedron \(P_1 P_2 P_3 P_4\).
