You know, after re-reading that, I think I get what you mean by "K". The 
idea here is sort of a mix of the two concepts. You get a K, by doing it 
the BFT way.

For terminology, let's refer to a single strip of material adhered to the 
space between two triangles, on one side, will be referred to as a "join". 
If you were to put another strip of vinyl on the opposite side of this 
join, you would create a "hinge". 1 sided = join, 2 sided = hinge. Where 
you have vinyl glued to the foam edge, you have a "gutter". Where the vinyl 
is only glued to the board, you have a "flat".

It folds like an accordion. From the outside, you would see a gutter, then 
a flat, then a gutter, then a flat...... This is important when trying to 
consider which way water will flow. Where will your gutters go and how will 
you make sure water doesn't follow them directly into your dome? I'm 
thinking of putting gutters on the top corners, with some overhang (like a 
spout). For every 'gutter', the opposite join will be flat. For every flat 
join, the opposite side will be a gutter. The great thing here is that 
instead of having to sew the vinyl together length wise, the fact that the 
boards won't sit exactly next together when you join them, there will be 
about 5mm gap. When you create a hinge with vinyl on the opposite side, the 
center of this strip will just become glued to the vinyl on the opposite 
side.

This is with a double miter:
  _______     _______
         \   /
  ________\_/________

This is with a single miter: 
  _______    _______
         \  |
  ________\_|________

That flat bit there in the middle will be where your vinyl will end up 
glued together. The top part is the 'gutter' join, and the bottom is the 
'flat' join. These alternate to make it fold up. Ideally, you'll end up 
with just one "flat" join to do when you get to the playa (plus the quads 
to eachother, then to the equilateral triangles, and the top square), and 
that can be done with BFT or whatever since you'll end up having to cut it 
in order to fold it all back up again. This would be where a zipper and 
flap would be another more permanent solution.

Hell, the vinyl and cement is so strong. I've thought about putting a small 
pipe in certain places to make a "pull this" type of setup. You pull a thin 
nylon rope and it unfolds the entire dome. Maybe next year ;-p

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