Mystic Puzzle Cube

This mysterious puzzle cube has various shapes and lines in a 4x4x4 cube made of smaller cubes that rotate and expand, much like a Hoberman sphere and a Rubix cube had a strange brainchild.
Although difficult to manipulate at first, it becomes easier to move and manipulate the individual segments, although the patterns this puzzle follows are especially difficult to trace...
Twice per day, a player may sit with the toy and work with it trying to make one of the faces line up. Perform an intelligence check (DC 16 + 1 per completed face). On success, they are able to piece together a facade on one of the sides, and upon completing it, it lights up the connecting lines and changes from dull grey to white lines, and a brief animation plays across the newly fit-together side. After that, the side remains changed, and something special may happen upon completing all 6 facades...
(in DnDBeyond, simply use one charge for each facade completed. another way to track the progress)

Facades