In the past few days I found myself having to find the position of face centres of a polygon.
Looking through the Maya documentations I find no MEL or Python commands that can do this. So I had to do a Google search the answer.
The most useful solution I found was from a discussion in Google Groups, in a reply by Justin Israel (who works in Weta Digital according to his Google+ profile):
Here is an excerpt of Justin's answer:
Here is another interesting article discussing how we can go about finding the centre position of a face: http://mayastation.typepad.com/maya-station/2009/11/where-is-the-center-of-a-polygon.html