A Three-dimensional Loom

In planning to make a smaller-scaled model of the type of sculpture I am interested in creating I have found that what I am looking for is something more akin to a loom, but adapted to three-dimensional development. There are so many intersections that I now imagine it easier, or more clarified to interweave the lines that form up the planes I want to create from all the way outside the subject area. This is like the proverbial notion of "thinking outside the box"

I had to wonder if I had at some point incorporated the little visual quiz I found in a book that regarded problem-solving in architecture.

Connect these nine dots using only four straight lines. [The solution I will post later.]