Summary

A little toy illustrating the decomposition of (a+b)^3 into a^3, 3 a^2 b, 3 a b^2, and b^3. This version has sockets for magnets to hold the entire assembly, but can easily be taken apart to count the pieces.

Instructions

The print file is sized in mm, so you'll have to scale by a factor of 10 if you're using MakerWare, which expects the units to be cm. The cube is held together by 3mm (diameter) x 3mm (height) cylindrical rare earth magnets. Orienting the magnets is done according to the rule:

small cube (a^3): all magnets are + (out)
tall, skinny boxes (a^2 b): all magnets are - (out)
wide, flat boxes (a b^2): all magnets are + (out)
large cube (b^3): all magnets are - (out)
The magnets should fit snugly, but I used a little JB Weld epoxy just in case. I suspect that you could also use superglue. I recommend printing the magnet insertion tools to help seat the magnets into the little holes.
This model is painted using Valspar plastic primer and Liquitex heavy body acrylic paint. So far, it seems to be holding up pretty well under handling.
This is a classroom manipulative designed to be used in a calculus class (or algebra class), as part of the project `Motivating First-Year Calculus with Robotics' supported by the National Science Foundation under DUE-12-45540. For more from this project, see my webpage.

Decomposition of Cube Manipulative