Starting from first principles you would end up with one coil per pole for a single phase winding. A 12 pole magnet system would have 12 coils per phase. As alternate coils are under alternate magnet polarities the connections to adjacent coils would need reversing ( or you flip alternate coils, same thing).
If you leave out alternate coils as you show that still works fine and no coils need reversing. You just alter the coil shape so that you use twice as many turns of twice csa wire for each coil and the end result is the same. That would give you a 6 coil 12 pole single phase winding.
Using conventional windings you will have to overlap coils to produce a 3 phase winding from either and that has been the standard way for many years. For axial flux machines where you need small air gaps and where the winding space is limited at the centre of the stator the overlapped coil is a challenge and it has been found that you get a better machine with far less effort if you go back to the original single phase concept and leave out half the coils of the basic half coil version ( leave out half of the coils of the 12 pole 6 coil version). That leaves you 3 coils per 12 poles and three phase will then go in as a single layer winding. It doesn't use all the stator circumference effectively ( there are unwound bits) but in real life there are so many compromises for wind power that when you consider all the issues this turns out a better winding. It wouldn't be the best way to wind a radial but the restrictions and compromises are different in that case.
Probably way off what you were looking for so ignore it if it adds confusion but this issue of pole numbers and coil numbers keeps cropping up and unless it is understood we shall be asked for evermore whether a certain pole and coil number will work.
Flux
