Rubik's Cube

Imagine a chest of many drawers - above and below, side by side -  such as a card catalogue cabinet.  Now imagine the cabinet with its drawers removed: one imagines an empty grid of supports and rails for the drawers.  But it ought to be possible to create a chest of drawers in which each drawer is supported and guided only by the surrounding drawers (or, at the edges only, by the cabinet).  I wonder if such cabinet of such construction actually exists.