Table S1.

Geometric definitions and characteristics of coupling variations shown in Figs. 6 and 7

Structure	Number and geometries of tubes	Coupling orientation and discussion
Canopy structure (Fig. 6A)	Thirty-two alternating tubes with α varying between $58°$ and $84°$. All tubes with $a=c=0.3$ m and $N=16$.	All tubes are coupled in the zipper orientation. The vertex angles α are calculated so the overall cross section follows a smooth planar curve (e.g., $\alpha =58°,84°,60°,83°,62°,82°$ for the first six tubes). This structure covers an area of $8.1\times 9.3$ m with a 2.6-m rise when deployed to 97% extension and can fold down to a size of $5.1\times 0.8\times$ 1.3 m at 5% extension.
Bridge (Fig. 6B)	Two tubes with $\alpha =55°$ (yellow) and six with $\alpha =85°$ (green). All tubes with $a=c=25$ mm and $N=5$.	Zipper coupling is continued in one direction only, where each tube is coupled on two opposite faces. The system remains rigid and flat foldable in two directions. The structure has a high out-of-plane stiffness.
Self-interlocking structure (Fig. 6C)	Twelve tubes with $a=c=25$ mm, $\alpha =75°$, and $N=5$ (red).	Zipper coupling is continued in one direction for each side of the structure. The tubes at the corners have zipper coupling in orthogonal directions (i.e., on two adjacent faces of the tube). The system is flat foldable in one direction and interlocks into a stiff conforming assembly at an extension of 96.3%.
Coupled polygonal tube (Fig. 7A)	Polygonal tube $N=5$: cross section with four panels of $a=c=25$ mm, $\alpha =55°$ (yellow) and two panels of $a=19$ mm, $c=20$ mm, $\alpha =40.94°$ (blue). One tube has $a=c=25$ mm, $\alpha =55°$ (brown).	Zipper coupling between the polygonal and the regular square tube can be done on any of the polygonal tube faces. The internal (blue) panels of the polygonal tube are defined to reach a flat configuration when external panels (yellow) are at $80\text{\%}$ extension. The structure is flat foldable only in one direction, but the internal folds (on blue) can change their polarity and can reconfigure the overall structural shape (Movie S2).
Zipper-coupled tubes with thickness (Fig. 7B)	Two tubes with $a=80$ mm, $c=40$ mm, $\alpha =75°$, and $N=4$. The thickness is $t=5$ mm on the thin part and $t=10$ mm on the thick part of the panels.	A technique of cutting out material (18) is adopted, allowing the structure to fold down completely to the minimal feasible thickness of $2Nt=80$ mm. The structure cannot extend to $100\text{\%}$ extension because intersection of the thick material will occur.
Actuator (Fig. 7C)	One tube of $N=6$ and one of $N=4$ cells, with $a=c=25$ mm, $\alpha =55°$ (orange). The rigid boundary is a bounded paper box (blue).	Zipper coupling along the middle section of the longer tube, while its ends are adhered to stiff boundaries. The zipper-coupled section prevents local and squeezing-type deformations. At the ends, the longer tube can undergo squeezing, allowing for the rigid attachment.