The last (for now) example in this series of bifoldable designs is a woven carpet. Will create a doubly periodic polyhedron that consists of the Miura tubes below (which are almost 50 years old!).
We begin with a corner type we call Double L
Four copies of it (using reflecions) can be combined into a translationa fundamental piece like so:
The tubes (of double length) emerge when we replicate this piece several times in both directions:
Above is its most symmetric state. This carpet does not need to be rolled, it can be squeezed in both of its translational directions, as below:
So you can push this Miura Carpet to any of the four sides of a room.