If you take a cube and unfold it you get a set of squares, called a planar net. There will be six squares, and they can be arranged in various ways. Usually people who want to make a box will have them connected in a "T" shape, but there are 10 other ways to unfold a cube.
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But if one wants to build a more complicated shape, for instance a dodecahedron, the problem gets trickier. That's because there are 43,480 ways to unfold one. But only a few will work in the self-replicating machine the two scientists wanted to build, because they were looking for the simplest combinations to fold the shape and maintain the best structural integrity. (When making a cube, for instance, you might want to minimize the number of edges that have to be joined rather than folded).
Menon, enlisted a couple of undergraduates - Margaret Ewing and Andrew "Drew" Kunas (also at Brown) -– to narrow down the possibilities. They built models and developed a computer program to find the optimal nets, and found six that seemed to work. They found optimal nets for icosahedrons (20 sides) octahedrons (eight) and truncated octahedrons.