The invention relates to a construction box (200) comprising a front wall (220), a rear wall and two side walls (224, 226), which delimit a construction box interior that houses a height-adjustable construction platform (210). The construction box (200) has dedicated travelling gear (250) integrated in to the construction box for propelling said box (2000 between a construction position, in which the construction box (2000 is positioned within the frame (150) of the system (100) to allow the shaped body to be built up and an additional construction box position, such as a construction box unpacking position, in which the construction box (200) is propelled out of the frame (150) of the system (100) to permit the unpacking of the built-up shaped body.