Mechanism-structure-mechanism transition of longer tubes with an odd . (a) Front and top views of the tube with ,, and deploying from configurations I to V. The corresponding folding angles are listed below the deployment sequence. The tube is completely concealed between IIIL and IIIR. Also see SM Movie S2. (b) Variation of dihedral angles vs. . The red curve shows that between IIIL and IIIR. (c) The nondimensional radii of vertices ,, and ()vs., in which the red curve shows between IIIL and IIIR. (d) Relationship among nondimensional radius of vertices (), , and . Some values of are listed alongside their corresponding curves. The shaded plane is where . Blue solid lines are for and grey dashed lines for (where physical interference happens). (e) Front and top views of the waterbomb tube undergoing structural deformation. At configurations IIIR to IIIL, the tube forms a concealed volume. Any in-between configuration, e.g., configuration III, requires structural deformation, as presented in the close up figure where the vertices are squeezed and distorted by each other. (f) Elastic strain energy vs. when the tube is modeled as a mechanism (in grey) and as a structure (in black) and their difference (in red).