This thing with the complicated-sounded name is a 60-sided, stellated shape, in which each face is an identical rhombus.
I mentioned this solid in a previoust post, after a teacher from Taiwan pointed me toward some excellent geometric models he created.
I love a math challenge, so I wrote up a free project to show how this thing is made.
So..... if you're pretty comfortable with SketchUp's Rotate too, and you aren't scared of working with groups and components, you too can create a rhombic hexacontahedron. And here's a twist: you can paint each of the rhombic solids that comprise this solid so that no color repeats around any vertex. Each vertex is surrounded by five rhombic solids, so you only need to use five colors.
Want to try it? It's my latest project on the Math Forum (free PDF download). As usual, I've posted a Teacher Version with some extra notes and comments, and a Student Version.
Anyone can design anything in 3D! http://www.3dvinci.net/