There are no tori. The original concept has inflated “cells.” A lattice tower could have tensairity beams making up the lattice.
Those are all unnecessary add-ons to the main idea, an inflatable tower, so are distractions.
More useful distractions would for example be the materials you would choose, the desired strength of the beams, their internal pressure, the tensile strength of the materials, resistance to wear and UV radiation, and so on.
And why an inflatable tower is interesting: the height you can make a tower is dependent on the specific strength of the materials you use. That means that a wooden tower has a higher theoretical maximum height than a steel tower for example. Perhaps an inflatable tower has a higher limit still, while being mostly air, so while being relatively inexpensive.