I have bugged people who claim to know about this, and am no expert but here are my 2 cents:
Residential 110 voltage is taken from the 240 supply. The transformer is middle tapped to make 2 110 legs. Look at it as a single long coil that is 240 volts from top to bottom but if you connect at the middle you can get 2 legs at 110.
For alternating current that changes polarity with a sine wave, you are getting half the wave in each leg. If you look at it on a graph, I think you get the positive half in one leg and the negative in the other.
The problem with 3 phase is you need the third phase to not be in sync with the others. So the only way to get the frequency right is to generate your third leg. You can run a motor on 2 phase that generates the third phase by coupling that motor with a generator. I think it might be possible to use a variable frequency device instead of the motor-generator couple but I now less about VFD.