Volumetric nonwoven structures: An algebraic framework for systematic design of infinite polyhedral frames using nonwoven fabric patterns

In this paper, we present an algebraic framework that can be used to construct a large class of 3D shapes and structures that can potentially provide unusual material properties. We formalized this framework as a 3D generalization of planar nonwoven textile structures that are used to mimic the woven structures. Our extension is based on the fact that it is straightforward to extend planar nonwoven textile structures into volumetric nonwoven textile structures, which we also call nonwoven volumetric fabrics. This property is essential because such an extension is impossible with planar woven structures. In other words, using this approach, it can be possible to easily produce volumetric structures that mimic the fabric behavior as if they were planar nonwoven textile structures, which is impossible to produce. These volumetric structures also correspond to regular & semiregular frame structures and are capable of representing previously unknown infinite regular polyhedra and flexible wood structures.