Mike, that is a superb carving.

Regarding the "3fold" Mobius,
I've been having trouble with a ribbon wrapped around a cylinder being a portion of a helix, NOT an ellipse,
even though the carving blank has elliptical ends. The math does not jive. I've been thinking about gluing up
a 60 degree triangle out of three broom handle pieces, and doing some wrapping, to see if the concept of ribbon wrapping is faulty.
I have not finished Boolean carving in Moi of a carving blank.

I located a nice tutorial in Adobe Illustrator of how to turn a hexagon with corner fillets into a flat picture of a Mobius 3 fold.
It has rounded corners, which again, are not helixes... http://www.deke.com/content/dekes-techniques-328-draw-a-m%C3%B6bius-strip-illustrator-0

It was fairly easy to use Blend to do a 4-fold (Non-Mobius) 3d model. I used a couple of g2 Blends, with the Bulge set to about 6 to 8 decimal places, by
repetitive number entry, until the Bulge was very close to passing through a certain point, say in the Top View.
I was thinking that it might be helpful to have a two stage bulge slider, for "fine tuning" to adjust decimal points?
The first slider could select two decimal points, and the fine tuning slider add on a few more decimal points.
(Unless there is some way to get a blend to pass through a certain point, or appear to pass through the point, in say Top View.)

I'm down to 1.1 mb upload space. Time to delete some files.

- Brian