Advanced Number Theory · Challenge problem

Triangles $ABC$ and $ABD$ are both equilateral with side length $8$, sharing the edge $\overline{AB}$, and are folded so that the dihedral angle along $\overline{AB}$ between the two triangles' planes is $90^\circ$ (that is, the two triangles no longer lie in the same plane). Find the volume of tetrahedron $ABCD$.