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I don't know the "correct" answer, but these are my thoughts: Three phase is the minimum needed to produce a rotating field. More phases would reduce the cogging of motors and make rectification easier, but the added expense of transmission (more wires and insulators) is probably the reason it is not used.
The 3-phase power is the most economical in delivering AC power using transmission lines. Using the same line voltage and same line current per wire, 3-phase can deliver 73% more power with 50% more wire (adding one more wire) over a single-phase line.
The reason we use 3 phase systems is because
1. It is much less expensive to transmit electrical energy to the user.
2. Generation of 3 phase electricity is no more difficult than the generation of single phase.
3. Equipment such as motors, transformers, and resistance loads perform more effeciently when using a 3 phase supply.
Note: 3 phase is also refered to as poly phase. Were as in a single phase circuit you only have the 50/60 cycle per second current. In a 3 phase system you would have 3 sequential phases 120 electrical degrees out of phase.
With 3 phase power motors can be started with out capacitors or inductive means making the equipment smaller and lighter.
A very simple reason would be cost, 6 phase would require 6 wires, 3 phase only requires 3 wires. Single phase requires 2 wires, but 3 phase only requires 3 wires - 300% increase in power for only 50% increase in cable costs - increasing the number of phases would only reduce this cost saving.
i wona ask u people that have any one of u know any links to the
ac fundamentals of electrical machine.as this topic is very important and at the same time it is very boring,so if u know any link where there is visual explanation of this topic so kindly let me know..