To form this polyhedron, I took a rhombic dodecahedron, and augmented each of its twelve sides with additional rhombic dodecahedra, forming a cluster of thirteen of these space-filling polyhedra. I then stellated this cluster thirty-four times, and this was the unexpected result.
The software I used to do this may be found (and tried for free) at http://www.software3d.com/stella.php.
RobertLovesPi.net 
That is a Nice one. If I let my eye “wander” a bit, it looks like the four smaller inverted cubes on the top rotate Backwards and become not inverted.
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Thanks for pointing that out — I can see this “cube jumping” too, now, but hadn’t noticed it before.
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