Although one could optimize the resolution by choosing a position that had the most verticality, this would make the printing take longer. Not only must the printer wait for each layer to set, but the tray must slowly adjust its vertical position before each layer can be deposited. A life-size replica of an australopith skull, for example, might take two days to fully print.
Another complication derives from the fact that the printer lays down layer on layer, bottom first. It cannot print the final product whole, but must prevent parts of it from collapsing with "support material." For example, if one wanted to print an upside-down cup, the print head would first lay down the round sides of a hollow cylinder. When the printer went to lay down the layers that would be the cup's base, without support material they would fall into the center of the cylinder, ruining the model. But if the printer fills the hollow center of the cup with yellowish, semi-transparent support plastic, then the base would print intact.
Depending on the support material created, there are different methods to separate it after printing is complete. Some companies produce support material that dissolves in water, but Delson's lab uses a crumbly material that can be knocked off of the modeling plastic by a blast of water. A water jet, housed in a large plastic box with a clear front, serves this purpose. Operators open a port on the box to pop in a printed model, and then stick their hands through the rubber-gloved portals into the box to pick it up and grab the jet's nozzle. Ready, aim, spray: the support material flies off as the model is turned to expose every surface, and within a couple minutes blue plastic is all that remains. To give the surface a final smoothing and cleaning, the model sits in a bath of sodium hydroxide for about 15 minutes.
Other 3-D printers simply lay down layers of powder, then add material to make the particles stick together. Some even create each layer by cutting it out of standard printer paper. Even metal can replace ink in a 3-D printer. As printing becomes an option for the manufacture of more and more objects, the technology may become even more ubiquitous—even if you're not in the market for models of monkey skulls.
What is the purpose of the fossil models produced via 3-D printing? More details in "3-D Printing Gets Ahead: Anthropologists Use Printing Technology to Model Fossils"