Johannes Kepler named the compound of two tetrahedra the “stella octangula,” thus helping make it one of the best-known polyhedral compounds today. This variant uses triakis tetrahedra in place of the Platonic tetrahedra in that compound. The triakis tetrahedron is a Catalan solid, and is dual to the truncated tetrahedron.
Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
RobertLovesPi.net 
would i be correct in assuming that this is also a stellation of the deltoidal icositetrahedron? i didn’t see it mentioned in the wolfram mathworld page on the subject, and i haven’t found anything online about it. i only have the free version of stella, so i don’t know if the stellation features work with the deltoidal icositetrahedron, or if the stellation diagram would allow for the shape depicted here. just hoping for confirmation from someone who knows a whole lot more about this stuff. thanks for all the work you do!
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I don’t think it is, but I could be wrong.
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