Further perusal of the work of David Georges Emmerich convinced me of the curious nature of Figure 2 in his French Patent (Brevet d'Invention) No. 1,377,290. (He didn't bother with U.S. patents.) It is a simple, yet unique, three-fold prism. After constructing it in cyberspace and putting it through the rigors of my software, it revealed even more curious and interesting properties. I constructed an equi-tendoned version. All adjacent tendons are oriented at 60°, 90° or 120° to each other and the prestress forces in all tendons are equal. It certainly should be regarded as one of the fundamental tensegrities.
You can peruse the datasheet for more details. This model was assembled on September 30, 2004. I'm obligated to architecture student Val Gůmez JŠuregui for kindly providing me with copies of Emmerich's French patents. Please be patient with my terminology. I refer to all tensegrities with three-fold or more rotational symmetry about a single axis as prisms.
The first time I attempted to construct Emmerich's prism in cyberspace, I got the topology wrong. The structure pictured below resulted. On developing a construction strategy for this structure, I realized that with both structures I was looking at two tensegrity tripods with the base of one tied to the apex of the other in a flimsy way. That made construction a lot easier since I could assemble the two tripods first (all tighter tendons) and finish by tieing the six flimsy interconnecting tendons (all looser by half). From this point of view, I saw the structure could be varied further by reversing the sense of the tripods with respect to each other. Due to interference problems, nothing much interesting resulted from this further line of variation.
Another datasheet summarizes the construction details for this structure. I couldn't come up with an equi-tendoned version. When I attempted to, I came out with something perfectly flat. I finally made the side tendons twice the length of the others. With that choice, adjacent tendons are oriented at 60°, 90° or 120° to each other as with the previous structure. The second model was assembled on October 5, 2004. This model is also available on the Tensegrity Viewer as "3-Fold Emmerich-Style Prism".