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.