Follow-up on the Space Frame

I appear to have fallen into a trap. Stephen Hyde says that the structure is what RCSR calls fcu and what EPINET calls sqc19. So how did I goof?

When I looked up at the space frame (photo below), I assumed that the edges parallel to the window were in a different orbit than the diagonal ones, and hence that there were two orbits of edges. So I looked for crystal structures with two orbits of edges:

• In RCSR, I went to the net search page and made the following entries: “1” for lower and upper bounds on the number of kinds of vertex (only one orbit of vertex), “2” for the lower and upper bounds on the number of kinds of edges (two orbits of edges),”3″ for the lower and upper bounds on the smallest ring (a graph theorist would call this a cycle), and “12” for the lower and upper bounds on the coordination (a graph theorist would call this the degree or valency). RCSR found five nets, four of which could be readily excluded from their pictures, and one with no picture (!) with space group Im-3m.
• In EPINET, I went to the net search page and entered “1” node per asymmetric unit (uninodal), “2” for edge transitivity (two orbits of edges), and “1” for nodes per unit cell (clearly from picture of space frame), and vertex degree exactly 12, not chiral, and I got two unlikely candidates.

But in fact, I did not realize that while the space frame looked as if the faces of the polygons (triangles and squares) chopped space into pyramids and tetrahedra, it was actually chopping space into octohedra and tetrahedra, all regular, and hence there was only one orbit of edges.

• In RCSR, if I entered one orbit of edges instead, I would get two candidates, one of which was fcu.
• In EPINET, if I entered one orbit of edges instead, I would get one candidate, sqc19.

So that’s how they work. You have to look at the crystal structure with the correct squint.