Can you explain more into it? A need a bit of a break down in regards to symmetry. Are you saying that a 3 phase motor needs doubles of 3?
It doesn't need doubles of 3, but you want to maintain symmetry and doubles of 3 is a good way to do this.
An induction motor will usually have slots rather than salient poles. You want an even phase angle increase from one slot to the next.
The phase angles that you have to work with are those supplied from your source, their inverse, and ones you construct by combining source phases (meaning coils from 2 phases sitting in the same slot).
One could imagine having slots or salient windings where the phase angle increases by 60 degrees per. This gives 6 slots per magnetic pole pair.
Or you could go up by 120 degrees per, giving 3 slots per pole pair. Past 180 degrees per slot and you actually reverse direction rather than going faster.
For any other number of slots per pole, you are either combining phases in a single slot (eg 5 turns of phase A plus 10 of phase b) or doubling things up, or intentionally introducing error.
The motor you posted a link to intentionally introduces phasing errors to get the desired pole count.
Hope that helps.