A tensegritry trellis is a wonderful thing. I've made 3 of these in different sizes for various plants. No math required and the results perplex the neighbors's kids. It looks like it shouldn't exist and it shouldn't work at all.
Process:
Cut 3 or more equal slats or rods of any material. I used old fence pickets.
Make a hole on both ends of each slat or rod.
That concludes the difficult part.
Now get wire or string, I used nylon tying string. Cut 6 equal pieces for your base. I usually cut these short compared to the length of the rods.
Cut 6 strings to be slightly longer than the length of the rods.
That concludes all cutting.
Now tie each string from one bottom hole to another bottom hole of a different rod (I'm not there with you, but any hole is the bottom hole, the other is the top hole. I tell my wife this but she gives me the look). Imagine making a ridiculous stick bracelet.
Now do the same for the top holes. Do it in the same order so stick 1 first, then 2 then 3 and back to 1. Congrats, this is almost done.
Now for the long strings. Currently your trellis is a pile of wood strung together flimsly. Stand it up, and tie a long string securely to one top hole. Then using your imaaagination twist the top triangle by 1 hole. Attach the other end of the string to the bottom hole of stick 2. Repeat from top 2 to bottom 3 and from 3 to bottom 1.... Did you notice anything? Yes! Magic! The darn thing is standing the fuck up! Nothing is actually holding the sticks together, just the strings and the other sticks.
Pock your trellis up and play.... 2hrs later... Now tie the 3 last long strings from stick 1 top to stick 3 bottom, stick 2 top to stick 1 bottom, and finally stick 3 top to stick 2 bottom. If I missed the order, don't worry, you're probably going to know the correct logic when you see it. This 2nd set provides redundancy and makes your wobbly trellis into a magnisifent, incredible, rigid trellis. Now stick it over a plant and tie the plant to it. Leave it alone.
Seriously dude, stop playing with it! Leave it alone. Make another one. You can make like 10 and give them to your neighbor.
So uh, question?
Why not do it with 5 strings? 2 strings that are each the length of 3 of your short strings, and the 3 long strings.
Would be much faster to tie, and easier to do with something like stranded wire, plus you could more easily adjust the positioning before adding the final set of strings.
And if you were worried about them slipping around, you can just do the string in a loop around each hole as you run it through.
I think you could, but you have to somehow lock their position. It's not immediately obvious but if you complete the structure like that it will just collapse. The various members of the structure must all be in pure tension or pure compression. Then again, I haven't tried that before, so it could actually work in some cool way.
That's easy enough, just loop the string around the stick after running it through the hole. Or be fancy and run in through the hole twice. Once the long strings are attached they will still be fully tense.