Truss as a tension/compression structure
The truss appears to use only rods. Rods provide both tension and compression. A well-designed truss can use rods for compression, and (much lighter) wires for tension. In this application, you can use carbon-composite rods for the compression members and truly light-weight fibers for the tension members. I suspect that the thinnest available Kevlar fibers will suffice for the tension members of the truss. So: a triangular truss would have three long composite rods, Nx3 very short rods, and 2Nx3 fibers. Or if you are brave Nx3 fibers. But this application does not need Symmetric triangular truss, because the forces in the three dimensions are not symmetric.
The trick here is to ensure that the rods and fibers have roughly the same coefficients of expansion (change in length with temperature.) Increased distiane between the rods will add weight but will reduce any warpage. Acceptable truss warpage, in turn, depend on how the truss orientation affects the mission parameters.
If all we need it a truss that points (approximately) "up", then at the extreme we need a single carbon rod. If we need more rigidity, then we need two or three rods. it is not clear why we need mor than two: gravity workss, after all.
Consider a two-dimensional truss of (say) one metre. Two 1-metre rods, separated at (say) 20-cm intervals with 100 mm rods. The rods are turn connected by digaonal Kevlar fibres at each junction. This two-dimensional structure is in turn stabilized at its midpoint by triangular outriggers in the third dimension, connected to each end of the truss with more kevlar fibres.