Wireless power transfer (WPT) for heavy-duty electric vehicles (EVs) are increasingly demanding in power level and power density. Multi-phase magnetically integrated coils are seen as a promising solution. This paper presents a general inductance model of the three-phase coupler, and derives the conditions of three-phase symmetry. Geometries including three-phase unipolar (3PU) winding and three-phase bipolar (3PB) winding are compared using multi-objective optimization. The results show that the 3PB coil has higher area power density while the 3PU coil is more advantageous in efficiency, core flux density and electromagnetic field emission. An experiment at 10 kW verified the high efficiency and low stray field characteristics of the 3PU coil.