This all began with a case of me trying to draw the right creases in a sheet of cartridge paper such that it has a concertina fold in two directions.
I realised it was the vertices rather than the faces that determine the folding and so began experimenting with them. Found that any number of creases to the vertex works so long as a) it is greater than 3 and b) the creases do not form an X through the vertex if there are only 4 of them.
Conclusion - taping together 6-crease vertices to make a flexible surface of solid sections, which can be squashed along its width but never completely flattened out.
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