The basic 12 pole 3 phase winding would be 3 single phase windings displaced 120 electrical degrees and would have 36 coils.
If you based it on a virtual pole single phase version you would achieve the same thing with 18 coils with twice as many turns of half csa wire.
Either arrangement can only intelligently be done with overlapped coils. Unless you can get the coil sides for all 3 phases into the air gap of a single phase you loose all the advantage of 3 phase except for vibration issues.
With a radial winding the overlapped coil design is almost universal.
I assume you are talking about an axial design and you will find an overlapped coil set up extremely difficult to do. There is just not enough room for the overlaps at the centre. You will need such long coil ends to do it that you will end up with more winding resistance than if you left half of the 18 coils out so that they ended up on a single layer.
If you accept the fact that it is virtually impossible and change the magnet spacing to make best advantage of the 9 coil arrangement you will have a better result.
If you try to directly compare a 9 coil with a 18 coil overlapped with the optimum magnet layout for the 18 coil, the 18 coil will win if you waste enough time and effort into squeezing the thing in as tightly as possible.
Even with the wrong magnet spacing for the 9 coil, 9 will win out unless you are an extremely skilled winder.
Flux