Here is an idea for fixing the vertex hoping:
http://www.geocities.com/fcmodelview/edgefix.jpg (copy and paste to browser)
To implement this, I think the easiest way would be to create a sub-routine
that connects an n-gon to an n/2-gon, and then call this routine for the
last "facets" of every slice. (Ie the "facets" closest to the vertex.)
