One embodiment of the invention is a slicing engine that generates two or more slices of a virtual 3D model given a slice plane. The slicing engine then determines connection points on each of the slices that indicate how the 3D model is to be reconnected by the user when the 3D model is fabricated. The slicing engine also determines an optimized layout for the various slices of the 3D model on fabrication material for minimal use of the material. The user is then able to “print” the layout on the fabrication material via 3D printers, and connect the various printed slices according to the connection points to build a physical representation of the 3D model.