Hint 5

First, place H. Insert it so that a gap remains in the middle, and position the pointed vertex at the center of the bottom face of the box.

If you try to place another H right next to it, you will get stuck quickly. Place T instead. If you try to match faces of the same shape, the orientation is uniquely determined.

After that, if you keep matching faces of the same shape, the way to insert each piece will continue to be uniquely determined.