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Those are some terrific ideas- thank you very much. Never heard of carbon tow, but it looks ideal.
As for tube width, I'm tempted to start with 2mm rod, if only for the excitement. Doesn't matter if the prototype breaks. And imagine a rack made of bits which are so thin that you can hardly see them!
I'm already mentally committed to triangles. Barnes Wallis is my inspiration. Getting compression will be a challenge. I'm no good at conceiving a design in my head. Didn't even pass Physics O level. So it'll be trial and error. I thought I might start by making something out of dowel.
nick_h.-
Where is that museum? Is it the one near Coventry?
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I don't want to be one of those naysayers (this whole thing is bonkers and I love your attitude towards this), but 2-3 mm tent poles in carbon might be awful.
Off the top of my head tent poles tend to be in the 10+ mm region. Stiffness scales a lot with diameter, so a 2 mm pole is going to be orders of magnitude less stiff than a more standard size
Ndeipi
Slappingpythagoras
Been having fun thinking about this rack.
I think you gain very little by using such thin tubes. I would probably use 10mm outer diameter (OD) carbon tubes for making a rack, or 8mm if I was feeling WW. I've no calcs to back that up, but it feels risky to just use 2-3mm tube without doing the calcs. And think of abuse loads, like someone stepping on the rack.
As for the brackets which connect the tubes at corners, you have many options.
Hose might make things a bit flexy depending on geometry - a cube would flex but a pyramid would be fine, so use many diagonal tubes. Triangles good, squares bad. If you took two short sections of hose, drilled at the middle and nut/bolted across each other into an X, you'd have a cheap weather proof 4-way connector. I'd use clear, bendy PVC tube for this.
You could also just drill holes into wooden blocks (or some other material), using ever increasing drill bits - i.e. in 0.5mm increments - to achieve an interference fit (push fit).
Or take fatter sections of rigid tube with ID matching main tube OD (like your ferrules). Join these using epoxy-soaked carbon tow. You'd want to do this with the tubes assembled into a mock rack, with some awkward jig involving tape and swearing.
You can also google "3 way PVC pipe fitting" if you don't mind 90 degree corners. Then spec your carbon tubes to match the sizes to achieve push fit.
With all of these solutions though, you'd need to hold (compress) the assembly under tension so that it doesn't dismantle during use. Like how tent fabric tension holds the poles into connectors. So one or two bungee cords would be an idea, perhaps made from inner tubes (can fasten these using buckles from an old rucksack).