The triakisoctahedron is the dual to a truncated cube. I saw it in Magnus Wenninger's book Dual Models (which I bought recently) and wanted one of my own just because the twisted dimples are so pleasing. He passes on a guess that there's several thousand stellated forms of the triakisoctahedron (I don't know if they've been fully enumerated since he published) and he provides two fairly pleasing examples. It's a pity the book (at least the soft cover reprint) has such poorly reproduced photographs since you can barely make out the details of his.
I used a lazy matlab and postscript trick to generate the printouts. After projecting the lines onto the page, I do a rough clip to get rid of the ends and print 12 to a page in a 3x4 grid.
My model is made from 50lb white card stock; it took just less than a week of intermittent work, counting the discovery that our home printer's feed problems were keeping it from printing accurately. (The first try showed me how not to put it together, anyway.)
Jesse had commented on how the light/color worked in the in-progress snapshot, and it made me wonder if I could pull off doing that deliberately. The model was completed early enough in the day today to make use of the dazzling winter sunlight coming through my window, so I set my sheets of sturdy-board down on my bed and played around. I was frustrated that my little prisms don't make a very long patch of rainbow, and that I didn't have a mirror to angle or stretch it, since it would have suited me better to have all the light boundaries caused by the shape it was hitting, rather than the end of the prism.
Next time I have an excuse to summon something from SciPlus I shall get a few bigger prisms.
I fixed the corner of the background on the first one with gimp's clone tool; otherwise they're only cropped and scaled.
Monty said "70's album cover" when he saw them.