This is the rhombic dodecahedron, one of the Catalan solids.
Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing eight triangular faces.
Here’s what it looks like with only the six four-valent vertices truncated.
Finally, here’s the fully truncated rhombic dodecahedron.
I created these polyhedra using Stella 4d, a program you can try for free right here.
RobertLovesPi.net 
must be interesting to figure out how the end result will look
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how do you do the valence-3 truncation?
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It’s been over a year since I made this post, and I simply don’t remember how I did that!
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