This thing includes a revised parametric script for generating polygonal facets for use in polyhedra. Several possible facets have been rendered. I know that the triangular, square, and pentagonal facets presented here are sufficient for building a wide range of shapes.

Thing http://www.thingiverse.com/thing:5028 extends this set with more types of facets, including spoke-like and polygonal facets for all shapes.

I've been wanting to create a very generic snap-together set of forms for MakerBot for some time. It would be awesome to have an algorithm that generates a queue of forms to slowly grow a very large procedurally generated object.

This is a revision of things http://www.thingiverse.com/thing:4893 and http://www.thingiverse.com/thing:4899, and an attempt to create a compatible set of snap-together primitives for building geometric forms. Thing 4893 set too large a scale to print pentagonal facets. Thing 4899 had a mathematical error which caused the different faces to be incompatible. This revision corrects that error.

Look up a polyhedron design, and print out the appropriate facets. Clean, and assemble. As long as you print out as many [+] snaps as [-] snaps, these pieces have a habit of coming together. These pieces can also be assembled into amorphous but rigid forms.

These pieces are snap-compatible with things 4893 and 4899, and shapes like the truncated tetrahedron (an octahedron with 50/50 triangles from two different scales), cuboctahedron, and icosidodecahedron, can be built by mixing triangles from one version with the appropriate polygons from another version. This creates a rigid solid that can serve as an interface for two different sets of piece sizes, if you are building some sort of amorphous structure.