Generalizing rigid-foldable tubular structures of T-hedral type

We introduce an alternative way of constructing continuous flexible tubes and tubular structures based on a discrete, semi-discrete and smooth construction of surfaces known as T-hedra in the discrete case and profileaffine surfaces in the smooth setting, respectively. The geometric understanding of this method enables us to generalize discrete tubes with a rigid-foldability and to extend the construction to smooth and semi-discrete tubes with an isometric deformation. This achievement implies a unified treatment of continuous flexible structures, like surfaces and metamaterials composed of tubes, and it is the base for a deeper study of zipper tubes and their generalization. Moreover, we discuss a potential application of the presented structures for the design of foldable bridges.

Automated summary

We present an alternative method for constructing continuous flexible tubes and tubular structures using discrete and smooth construction of surfaces known as T-hedra and profileaffine surfaces respectively. This method allows for generalization of discrete tubes with rigid-foldability and extends the construction to smooth and semi-discrete tubes with isometric deformation. Our achievement enables a unified treatment of continuous flexible structures and provides a basis for deeper study of zipper tubes and their generalization. Furthermore, we discuss a potential application of these structures in the design of foldable bridges.