Three phase vs. six phase vs. limiting case power transmission

twice as much power twice as much copper twice as many insulators. power poles need to be twice as strong, switch yards twice as big. no net gain.

Assuming you use the same amount of copper as 3 phase just more finely divided, at some point you need to swap to flat conductors aligned radially to avoid short-circuits. skin effect will do something to this.

also, you can't have more conductors than there are turns on the power transformer.

My understanding is that conductor efficiencies improve with the more phases, and phase to phase potential become lower. So for the same copper I don't see why poles need to be any stronger unless the number of insulators determine the capacity of the pole.

If you use conductors > 1" then smaller conductors with a polyphase transmission system would have less loss from any skin effect.

Best shape for conductors to reduce field strengths would be round. You might use square for transformers.

Not sure what you are saying here.

By judicious design, its not difficult to create say 6 phases from 3 just with transformers.

We could keep the thought experiment simple to start and just imagine there is a non-reactive load connected to a set of lossy (resistive) conductors with the same resistance, and to the power-transmitting end connect ideal AC voltage sources of some peak value V, offset in phase by 120 degrees for 3 phase, 60 degrees for 6 phase, etc. and not worry about geometry or conductor size for the moment; 50/60 Hz is more-or-less DC over pretty long distances as far as skin effect and transmission line effects are concerned.

is there a limiting value of the amount of power you can transmit as the number of sources in superposition feeding the load goes to infinity and the phase difference between them goes infinitesimal. I assume there must be such.

That is what I was taught many moons ago, and that 3 phase was a good compromise.

Unfortunately I can't find a link to this theory with a quick google. Hence starting with "My understanding" and happy to be proven wrong.

wouldn't the limiting case be the same as using DC? m

Yes, that was my understanding.