I think this would be considered a Truncated Icosahedron star! I used the pieces from the Truncated Stellated Octahedron but thirty of them... it looks awesome!
Found a really cool pattern for a Truncated Stellated Octahedron, this model actually is more of a Hexahedron because it only is six pieces... but that is not the proper term. Not really sure what shape this is!
Little Octahedron (square diamond shape) I made out of some very cool shiny paper. It got a little too small so the pieces were not as tight as I would have liked though.
I found this pattern after much browsing on different origami sites, it was designed by Mette Pederson. This one is using 18 pieces although I saw some people using 19 instead... the paper is actually the inside of different envelopes! I had been saving the paper for something cool and this seemed like a perfect use :-)