I’ve been reading this one site about tensegrity structures, and the author starts by explaining them in terms of space frames. So far so good, except I’m wondering if he’s flat-out wrong about something:

On this page and the two following, he claims that there are only three ways to make a 3D symmetric lattice consisting of straight lines extended indefinitely. One is the familiar cubical lattice, the second makes a pattern of octahedrons and cuboctahedrons, and the third tetrahedrons with truncated tetrahedrons. See linked page and following for examples.

But I’m certain that’s not the only three ways. For example, what about this pattern of tetrahedrons and octahedrons? Unless in a way that’s non-obvious to me it’s geometrically equivalent to one of the others; or is there some principle involved that makes it ineligible for the purposes the author was discussing?