Thanks Gardar. I'm not having any trouble with finding the BMW part number - more that when I search for replacement parts, I get an array of options that I cannot confirm will fit.
E.g. - a search for BMW 64557786706 can yield: -
This -
https://spareto.co.uk/oe/bmw-64557786706
and this -
| Spare Auto Parts New Zealand [2187-ST2] - PULLEY IDLER
and this -
http://www.amazon.com/64557786706-Pu.../dp/B00HCO7DJI
What I'm trying to determine is which of the "pulley wheel only" options are the correct fit, hence the question about diameter etc.