Basically, saying that the 3-phase supply is not a replicate of 3 times the single-phase supply. The 1-phase supply is between 1 line- and neutral. The 3-phase supply we obtain is not like measured between 3 lines-Neutral (like (R-N = 220) + (Y-N = 220) + (B-N = 220) = 660 IS WRONG).
Rather the supply we get in 3 phases is measured between either of the two Lines wise ( R-Y or Y-B or B-R) & at a time when one isn't in action. So, calculating the voltage between 2 lines is like adding the two-voltage source, but the point to make note of is they all are 120 phases shifted to each other (i.e. either lead or lag by 120 degrees in a Sine wave corresponding to them).(Therefore, sin 120° = √3/2 =0.866 .)
Now if you connect any two of the 3 lines it will behave just like the 1-phase supply only. It will Run to give you o/p but with a loaded configuration & will go on heating the windings finally burning your appliance to fumes.
Now in the 3-phase system, we have voltages added of the 2 line i.e. R=230 +Y=230(120 shifted)
So total voltage = 230 + 230sin 120° (+-120 degree) = 230 +230 (.866) =230+200=430
i.e. 420-440 variable
Motors that use a three-phase supply (440) still only use two phases per coil (one on each end) but use different pairs of phases in sequence for each winding. That is why the rating is still 440v not 660v (220+220+220).
This is because the voltage in a three-phase system is measured between phases, not between a phase and neutral. The voltage between any two phases in a balanced three-phase system is √3 times the voltage of a single phase, which is why it's 440 volts and not 660 volts.