From Trammell Hudson's Projects
@mathgrrl introduced me to the Catalan solids and I used my unfolding STL tools to produce some fold-up cardboard versions. These are both pentagonal icositetrahedrons, which have the property that all of the faces and vertices are the same, but the edges differ.
The first was a solid one for a test out of fairly thick cardboard. It didn't cut or bend as smoothly as I had hoped. It is available as thing:900701.