This is more a thought experiment than a buildable structure. I wanted to build some things using Snelson's X-Module and decided to start by imagining what an unending column composed of such modules would look like and how it could be designed to give acceptable clearance to the struts. By doing this, I'm able to concentrate on designing how the X-Modules are linked together without having to deal with how the column ends. This thought experiment could also be viewed as examining a segment of a torus composed of arbritrarily large numbers of stages.
A tower based on the X-Module seems problematic to me since it would be difficult to get it to stand up. It might make an interesting fence or similar horizontally-oriented structure. Just for fun, I designed this column so the struts are exactly at 90° angles, as can be seen in the top column in the rendering above. As can be seen, the clearances between the struts are very good (clearance per unit strut length = 0.203). I think this is a little exagerated since a practical structure is more likely to have the struts longer, and I don't think the distance between the struts will increase proportionally as the length of the struts relative to the girdling tendons is increased. This design was completed March 16, 2004.
In Spring 2006, Netherlands high school student Matthijs Hogervorst completed a five-stage column based on these numbers:
Photo courtesy of Matthijs Hogervorst