Abstract: A polyhedral puzzle made up of a central body element, and intermediate and external body elements and characterized by the intermediate elements and the external elements being constructed and arranged to move in planet carriers and planet gears fashion respectively relative one to another in the polyhedral puzzle assembly and for selective displacement of the external elements over the entire outer surface of the assembly. This cubic puzzle includes a central body of polyhedron shape on the faces of which are pivoted the intermediate body elements slidably carrying the external body elements.