I've started work on 3D printing lesson plans, coordinating recently with Stratasys, the maker of the 3D printers used at UVa. I'm happy to see that using Sculptris in our Saturday Enrichment 3D class really gave kids a solid and fun introduction to the basics when it comes to printing concepts and design, such as:

Additive Manufacturing = this is the scientific term for 3D printing, and it's named so due to the way designing a project works, where you add layers to your design as you go along. When we used Sculptris, you could see how adding a new brush or changing a brush property automatically applied this change over whatever you'd already created.

Mesh = 3D mechanism that allows you to create a smooth solid object through polygon division. Sculptris uses triangles and when you have the wireframe tool turned on, you can see how small the triangles get (division) each time to apply a brush action to an area. Optimal printing requires a smooth object without holes in the mesh, but the challenge is in creating such an object using the least amount of polygons (or triangles) as possible, because the more polygons you have, the bigger the file size and therefore, the longer it will take to print, if it prints at all depending on the printer's capabilities.

STL files = the common standard for 3D printing file formatting, known by the full name "Standard Tesselation Language"

As exciting as it is to create, the standard for beginning projects is to keep it simple, with single piece design, Stratasys suggesting creating spinning tops, which of course, you can design many different ways and measure performance to evaluate design approaches. I'll work on creating some this summer to check it out!