Ok, I have a totally twisted way to do this in Chimera.  Select the ring atoms, say with the mouse (shift ctrl click each atom).  Then

measure inertia sel

This shows an inertia ellipsoid centered on the atoms.  Then how about just stretching the ellipsoid perpendicular to the plane and squeezing it in the plane to make a cigar?  I thought I could do that with the sop transform command, but no such luck.  So instead make a second inertia ellipsoid, rotate it, then show the rotation axis:

measure inertia sel

turn 0.428,0.497,0.755 90 center #2 model #2 coord #2

In the turn command I used the axis taken from the reply log given by the measure inertia command (v3, axis with largest inertia).  Picture attached.  Ok, this should be easier in Chimera!

Tom