I have written about the compound of three cubes, the most difficult question on the Mega Test, and of course used by MC Escher at one point, in "Waterfall," which was on lot of dorm walls when I was in college.
Ganzir just sent me this, so I will pass it along.
Good Luck!
Ganzir also tells me that this interior space is a Rhombicuboctahedron
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