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Well, all I can say is that I am unable to replicate a "nice"
result. Either we have different notions of what "nice" is,
or I'm doing something wrong.
Here's a photo of what I get when I try it:
Your elementary school fold is also under stress as it transitions.
I don't want to get into a big debate about the symmetry.
-- If I wanted to make the result symmetric, I could have done so.
-- If I wanted to make the result non-symmetric, I could have done so.
-- When I just fold the cube without thinking about it and without
trying to bias the result, it is not quite symmetric. I get a Z- fold
on two sides, and an L-fold on two other sides. You can see one of
each in the photo.
We agree that the 100% folded state is symmetric and stress-free and
that the 100% unfolded state is symmetric and stress-free. My point
is that when the thing is about 1/3rd open it is under lots of stress
for no good reason.
My point remains is that the Savage design does not fold nearly as "nicely"
as the plain old elementary-school fold discussed previously, according
to my notion of "niceness".
If the top and bottom of the Savage design remain symmetric, i.e. square
and flat, then there is lots of compressive stress in the edges that
are destined to become the vertical edges. The causes them to crumple
as shown in the photo. If this were *my* lead balloon, I would be very
unhappy with this ... given that the other scheme is AFAICT in every
way simpler and better.