Professor Jan Boeyens <jan@hobbes.gh.wits.ac.za> and Debora Evans wrote a 
program to do exactly this for any size ring.  It is called conpuc.  I 
takes it's own cartesian coordinate input, that I'm sure is easy to convert 
from MM3.

The reference is:

  D.G.Evans, J.C.A.Boeyens, "Conformational Analysis of Ring Pucker", 
  Acta Cryst. (1989). B45, 581-590

and the program source is available at:

  ftp://hobbes.gh.wits.ac.za/pub/conpuc/