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I'm tempted to knock out some quick FE models to find out
Good luck with the optimisation. You have up to 15 tubes, for each of which you can choose the diameter¹ and wall thickness². You have at least 5 different main topologies to dispose these tubes. All that's left then is to find the least amount of material required to achieve a given stiffness.
¹Major and minor diameter separately for elliptical tubes, plus the option of having the major axis vertical, horizontal or transitioning from one to the other along the length of the tube.
²Which can also be varied along the length of the tube either as a continuous taper or a series of butts.
³There's a footnote 3‽ Yep, the tubes can be tapered in diameter too. Or they can be shaped in almost any way other than circular/elliptical, possibly varying along the length.
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gbj_tester
Hovis
I would think a double diamond would be stiffer vertically, but less stiff laterally than the other variants. I'm tempted to knock out some quick FE models to find out.