The invention relates to a method for constructing a molded body from photopolymerizable material under application of a lithography-based generative manufacturing (Rapid prototyping); a layer of liquid photopolymerizable material is polymerized in a light exposure area with a specified contour by means of light exposure on a construction platform (1, 2, 3, 4); an additional layer is defined on the polymerized layer; the most recently defined layer is polymerized in a light exposure area with a specified contour of the most recently defined layer by means of light exposure; and the last two steps are repeated until a molded body with a defined shape is formed by the sequence of outgoing degenerate layers with layers specified contours. Color is applied onto at least one layer in the specified contour, wherein the construction platform is suspended in a movable manner and is conveyed to a color application station (30), where color is applied onto a layer, by means of a moving process after the layer has been polymerized in a polymerization processing station, in the color application station color position is selectively applied to the most recently defined layer, and the construction platform is then returned to another polymerization processing station. The movement of the construction platform between different processing stations is carried out by rotating a drum-shaped support (6) about a rotational axis, said support holding the construction platform at the circumference thereof, and processing stations are distributed about the rotational axis of the support in the rotational direction.