Puzzle Box: Spiral

Here are the views of a 11x11x11 puzzle box from all sides.

The top face has a shallow hollow (about 1/2 a unit deep), with a spiral pattern printed inside of it. There is a black square on the corner of the hollow. A small hole (too small for your fingers) extends behind the plexiglass front face.

The front face is clear plexiglass, and you can see the inner workings of this side. A horizontal fault line extends across the entire side. A spring loaded L shaped piece can be seen.

The right face has a dovetail shaped fault line, with a lock joining the upper and lower halves. The lock requires four digits, to be entered into a two by two arrangement of squares.

The back face, similar to the front face, is also clear plexiglass, with a horizontal fault line. Two pins that freely move due to gravity are stuck inside ‘4’ shaped channels.

The left face, similar to the right face, has a dovetail shaped fault line. There are two slits at the bottom that extend behind the bottom plexiglass face.

The bottom face is plexiglass, and several polyominoes can be seen behind, forming a rectangle. There are square shaped hollows at every corner of this rectangle. These polyominoes are opaque and have etchings on them that can be seen from one side. Despite being inaccessible to your large fingers, you seem to have mental control over the movement of the polyominoes (provided that such movements are physically possible). This telepathic power only seems to work on the bottom face, unfortunately.

While solving this box, imagine yourself trapped in an empty white room with no tools.

Open the box by separating the halves.

The following hints are for the lock puzzle.
HINT 1:

HINT 2:

HINT 3:

HINT 4:

HINT 5: