Three phase power has several advantages over single phase power, including smaller transformer size and weight, and simplified motor construction. Four phase power, which is actually two phase power with the phases in quadrature (90° apart), doesn't really offer any advantage over three phase power but requires an extra conductor. Some experimental work has been done with 6 and 12 phase power, but these have never been put into common usage. When you consider the cost of long transmission lines from the power source, three phase power is the best alternative.