This is not the only truncated form of the rhombic dodecahedron. In this polyhedron, square-based pyramids have been “truncated away” from the rhombic dodecahedron’s four-valent vertices, but the three-valent vertices remain untouched.

If this truncation is done in such a way as to leave the hexagonal faces equilateral (which is not done here), so that all edges of the polyhedron have the same length, the result is called a “chamfered cube.” This closely-related figure may be seen at https://en.wikipedia.org/wiki/Chamfered_cube.

[Image credit: this rotating model was created using Stella 4d, software you can find right here, with a free trial download available.]