A device for forming 3D bodies, in particular pieces of furniture, by additive material application. In particular, the device has a support, on which the volume body is formed, an application unit, for building up the 3D body on the support by additive application of material, and a tool carrier with a tool holder, in which the application unit is mounted. The tool carrier is in this case designed in such a way that the application unit mounted in the tool holder can be aligned in five directions by moving the tool holder with respect to the support.