I figured that if silnylon only comes in at a maximum of 65" widths (as on suppliers' websites), then you end up having each triangular panel being a maximum of 65" tall. If the base (or edge) of these triangles is indeed 84" (point to point), then the sides (or ridge lines) could only be at a maximum 77.4 inches. This figure doesn't take into account seam allowances, but it is darn close to the 78" ridges that Travis measured.
So, assuming 65" wide bolts of silnylon, the panels on the Trailstar would be triangles that are 84" at their base and 77.4" along their edges (which form the ridge lines of the shelter). Jim, your math says that the height of the triangular panels should be 68" not 65", but perhaps the panels are just being stretched tight – 6% stretch doesn't seem too unreasonable. There could be even more leeway here if the "36 inch" height figure is not taken too literally (for example, if the actual height was 34", then there would only need to be 3% stretch to account for the difference. The added length of tie-outs and where the measurements are actually taken further complicates the matter.
At this point though, it seems safe to assume that 65" silnylon is used to make the largest possible triangular panels (84"x77"x77"). It would just suck to try to make one of these, either out of silnylon or cuben, and find out the geometry just doesn't work when pitched. Making one out of cuben… seems to me that eliminating most of the cat cut on the ridges would be a good starting point.
Travis, the ideal way to measure it would not be along the actual seam. Because of the catenary curve, that seam is going to be longer than the actual side of the triangle. The best way would be to pitch the tarp (taut but trying avoid stretching it too much), and then take a piece of string and stretch it from a corner tie-out up to the apex of the tarp and measure the length of that string.
Although… now I'm questioning whether there is a cat cut at all between each of the side panels.