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 \(P_1 P_2 P_3 P_4.\)
Note: A tetrahedron is called regular if all the edges lengths are equal, so all the faces are equilateral triangles.
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