This sponge is a lie. Or, at least, it's not quite what it pretends to be.
In a way it's an analog of a Level 3
Menger Sponge, for a
Rhombic Dodecahedron. But more honestly, it's 12 copies of a Level 3
Sierpinski Carpet, squashed into rhombuses and arranged around the faces of a Rhombic Dodecahedron.
Don't think about it too hard. It looks awesome.