Make a copy of badge for the s-shaped badge holder
Change badge2 to have badge inserted diagonally and held in with ring
Modify to remove extra room for sliding badge.

Badge will now need to bend to be inserted, because opening_height*2 <
badge_height.
Add a little loop on the corner for the ring
Add cones to smooth transition
Nudge the ring to overlap a little more (and add code for smoothing
cylinders)
Version sticking out more with smoothing cylinders
Go back to version without cones, and increase loop size