I have completely revised my answer considering the information in the question and the comment:
I think it has more than 10 pole pairs but not sure exact number. I know it because it takes more than 10 electrical commutation cycles to complete one mechanical revolution.
The photo seems to indicate this is a wye connected motor with the neutral point brought out for external connection. There appear to be three individual stator-winding conductors attached to three solder points at the bottom of the picture. Just to the left of the bottom, the ends of the three conductors appear to be twisted together and soldered to a fourth solder point. It is also obvious from the photo that this motor has salient-pole windings in the stator. The rotor magnets could also be considered to be salient poles.
The apparent construction is then a doubly-salient permanent-magnet motor (DSPM motor). A DPSM motor can have different numbers of poles on the stator and rotor. The stator could have 12 poles with the phases distributed alternately among the poles. It could also have 6 or 4 poles with 2 or 3 phases making up each phase. If the stator can be disconnected from the driver, a small DC voltage could be applied between each phase and neutral to determine which coils are magnetized by each phase and which are north and south. A diagram of the results can probably be used to determine the number of poles.
With a DSPM motor, the number of poles in the stator does not have to match the number of poles in the rotor. In that respect, a DSPM motor is similar to a stepping motor. There may also be a similarity to some switched reluctance motor designs.
To determine the number of poles in the rotor, count the number of poles by carefully moving a magnet around the inside circumference and noting attractions and repulsions. Take note of Bruce Abbott's advice about the possibility of demagnetizing with a strong magnet. You could just use a piece of steel, but you would have difficulty finding repulsive regions. Perhaps a very small magnet that is not Neodymium would be ok.