Here is a design for a double-layer tensegrity dome composed of edge-connected three-fold prisms. The tensegrity dome technology I promote uses tensegrity tripods as its basis, but it turns out the method I use to generate domes based on tripods also works for generating domes based on three-fold prisms. This particular dome design is an example based on a frequency-six tensegrity breakdown of an octahedron. I've introduced a little fog into the picture so the foremost portion is easier to examine.
The hardest part of getting things to work was figuring out how to interconnect things at the vertexes of the basis octahedron. After some puzzling, I came up with a method which is pictured below where the two prisms "A" and "B" meet at an octahedral vertex. I undid their prismatic topology to a certain extent at their meeting point so that things could be attached without the members running into each other.
If I were to develop this design further, I would fix it so the outer ring of points at the bottom is attached to the ground in addition to the inner ring. This would make the structure more rigid I think. I completed this design on May 14, 2004. For a further examination and comparison of trusses based on tripods with those based on prisms, see Appendix A of my book, A Practical Guide to Tensegrity Design.