The properties of most materials depend on their composition, but when a material's crystal structure changes, its properties also change drastically. Such behaviour often occurs in smart materials and polymers, the properties of which alter in response to external stimuli such as temperature or pH. Architected materials, also known as metamaterials, can mimic this behaviour by containing engineered structures. Many automated technologies would benefit from the use of reconfigurable architected materials. On page 347, Overvelde et al.¹ report an algorithm that allows one class of these materials to be designed and their deformation properties to be investigated.

Advances in manufacturing technologies have enabled the production of architected materials that would be laborious or impossible to make using conventional methods, at multiple scales. These technologies can fabricate complex mechanical components of materials, print 3D scanned objects and prepare structures that can even 'program' the stiffness of a material.

Such advances have diverse applications, but have been particularly useful in robotics. To build adaptable robots that interact easily with their environments, designs are needed that enable transformation of machine assemblies and shapes. Such reconfigurable robots have been made using hardware components that reshape according to the task in hand or the environment^{2, 3, 4}. The greatest challenge in designing such robots is determining the geometric and mechanical parameters of both the machines and their components needed for various tasks and environments.

One of the principles that can be used to address this issue is origami-based design^{5, 6, 7, 8, 9, 10}, in which architected materials are made by folding sheets into shapes along pre-defined creases. However, practical difficulties arise because not all origami-based structures can be reconfigured, and it is not obvious which ones can. Overvelde and colleagues use an algorithm to work out some of the reconfigurable configurations that can be achieved for origami-based modules of architected materials. The work focuses on prismatic origami structures and their 3D-array patterns, which are relevant not only to the design of modules for origami robots, but potentially also to metre-scale architecture for buildings, and for understanding the behaviour of many chemical reactions and materials.

The concept of reconfigurable and controllable origami-based architected materials is not new^{11, 12}. Indeed, Overvelde et al. previously reported¹³ an algorithm that allowed them to design and prepare a highly reconfigurable architected material inspired by snapology (a form of origami). The authors now use that algorithm to further explore the achievable degrees of freedom of origami-based architected materials, by considering prismatic geometry configurations of their snapology structure.

To understand the process involved, imagine extruding all the faces of a polyhedron to form prismatic pillars of equal length (Fig. 1). The resulting shape can be combined with other extruded prismatic structures by matching up prisms that have the same cross-section, thus forming the basic unit — a cell — of an architected material. The cells can then be tessellated to form the material itself. The authors find that the deformation modes of the architected materials predictably depend on the tessellated patterns of the cells and on the shapes of the extruded prisms. Overvelde and colleagues also provide an algorithm to determine the geometric parameters of cardboard prototypes that can be constructed as models. These structures include systems of triangular and hexagonal prisms, of octahedra and cuboctahedra, and of triangular prisms alone (see Figure 1 of the paper¹).

Architected materials contain specially engineered structural elements. a, Designs for origami-inspired architected materials can begin by identifying a repeating unit composed of polyhedra. b, Prismatic pillars of equal length are extruded from the faces of the polyhedra. c, The resulting shapes are combined into the basic unit — a cell — of the material by aligning prisms that have the same cross-section. d, Many of the cells are then tessellated to form the architected material. Overvelde et al.¹ report an algorithm that allows the rational design of reconfigurable prismatic architected materials and determines their modes of deformation.

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The researchers go on to show that not all the faces of the original polyhedra need to be extruded to be part of a cell, and that the deformation modes and mobility of the architected materials change depending on which faces are extruded. This offers a means of reconfiguring the cells to alter the materials' properties. The authors clearly demonstrate that the geometric parameters of the cells dictate the overall motion, functionality and physical space occupied by the materials. Indeed, the authors' algorithm can determine the mobility and deformation modes of the prismatic architected materials.

One of the appealing aspects of Overvelde and colleagues' algorithm is that it describes architected materials defined by simple structural and physical rules: the entire deformable architecture is made up of a single type of cell. The idea of using tessellated and repeated cell components resonates with the design principles of origami and of modular robots.

The controllability of the architected materials could be increased by introducing 'lockable' joints that can be made either rigid or flexible, rather than using passive elastic hinges as in the current work. The authors manually handled their prototypes to demonstrate the deformation modes (see Supplementary Information for the paper¹), but the size and direction of the applied loading stresses are constrained by the flexibility of the hinges. Having actively lockable joints could further validate the effects of reconfigurable modes under various loadings. It would also allow the robotics community to discover origami platforms that have controllable degrees of freedom dictated only by the geometric constraints of a repeating cell module.

Building interactive, versatile hardware that has a high degree of freedom and mobility remains a key design challenge for many automated instruments and robots. Overvelde et al. introduce a robust strategy for designing reconfigurable modes for architected materials. Potentially, many more designs for architected materials will be made possible by using different assemblies of convex polyhedra. The authors' algorithm might well translate into strategies for designing automated systems, including diverse origami robotic systems.