157. It is known about the tetrahedron that all its faces are similar, but not all are equal to each other triangles. In addition, any two faces have at least one pair of equal edges, not counting the common edge. Find the volume of this tetrahedron if the lengths of two edges lying in the same face are 3 and 5.
157. If two unequal and similar triangles have two equal sides, it is easy to see that the sides of each of them form a geometric progression, and the sides of one can be denoted as $a, \lambda a, \lambda^{2} a$, and the other as $\lambda a, \lambda^{2} a, \lambda^{3} a$.

Further, if the sides of a triangle form a geometric progression and two of them are 3 and 5, then the third side is $\sqrt{15}$ (in other cases, the sum of two sides will be less than the third). It is not difficult to prove then that in our tetrahedron, two faces are triangles with sides $3, \sqrt{15}, 5$, and the other two have sides $\sqrt{15}, 5, 5 \sqrt{\frac{5}{3}}$ or $3 \sqrt{\frac{3}{5}}, 3, \sqrt{15}$; accordingly, the problem has two answers $\frac{55 \sqrt{6}}{18}$ and $\frac{11}{10} \sqrt{10}$.