Here's the thing: That structure is composed of
truncated octahedra.
Take a look at the very bottom of the article. The distance between the center of that polyhedron and the centroid of its faces are
different depending on which type of face (square or hex) you're talking about. This is relevant because this means that even if two units are adjacent to each other (i.e. on nodes sharing a face), you don't know how far apart they are. In other words, if two creatures are adjacent on nodes sharing a square face, they're
farther apart than if they shared a hexagonal face. How do you handle a situation like this in a game? It's not very clear at all.
If I'm reading that Wolfram Alpha article correctly, the distance between two units on cells sharing a hexagonal face is √6 whereas the distance between two units on cells sharing a square face is 2√2, assuming that each unit exists in the center of the cell, which is reasonable. In terms of a ratio, the ones sharing a hexagon are about 0.886 times as far apart from each other as ones sharing a square. This difference in distance is significant - almost as significant as the difference between the distance between two adjacent squares and the distance between squares diagonally. And honestly, even if the difference weren't that significant, it would still be there screwing up calculations if you didn't handle it mathematically.
So yeah, truncated octahedra seem interesting, and it avoids the case you have with cubes where cells meet at points/edges, but it introduces a much
harder case to deal with, since moving one cell isn't even necessarily the same distance even if the cells are adjacent, and creatures adjacent to each other aren't a constant distance apart. Also, the fact that it has different types of faces is just plain confusing.
Oh, and I just realized another issue: It's essentially "staggered" in all dimensions, so I don't see any way to slice it up into usable cross-sections, which is what we need (z-levels).
And now my head hurts from figuring all of that out.