In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.he physical properties of materials are largely determined by structure: atomic/molecular structure, phase distribution, internal defects, nano/microstructure, sample geometry, and electronic structure. Among these, engineering the geometry of the sample can provide a direct, intuitive, and often materialindependent approach to achieve a predetermined set of properties. Metamaterials are fabricated based on geometric concepts (1-16). In two dimensions, periodic geometries have been adopted to tune the mechanical properties of membranes (3-8, 10, 12-14). From simple shapes such as circles (3), triangles (6,7,12,13), and quadralaterals (4, 5, 14) to more complex shapes (8, 10), a broad range of mechanical behavior has been observed, including pattern transformation, negative Poisson's ratio (auxetic), elastic response, and isostaticity. Origami and kirigami, the arts of paper folding and paper cutting, create beautiful patterns and shapes that have attracted the attention of scientists to two-dimensional materials (e.g., graphene, polymer films, and so on) (11,(17)(18)(19). However, application of conventional origami and kirigami approaches to achieve desired material response requires complex cutting and/or folding patterns that are often incompatible with engineering materials. In this paper we propose an advanced approach to the design of two-dimensional structures that can achieve a wide range of desirable programmed shapes and mechanical properties.This study starts from the question, Can we design twodimensional structures that can be formed by simply cutting a sheet, that can morph into a specific shape? In nature, many biological and natural system (20) can be found that use hierarchical structure to produce different properties and/or shapes. One such example is a stem cell. An embryonic, pluripotent stem cell can differentiate into any type of cell in the body (21). By recursively dividing, the stem cell can transform into particular cell types or remain unspecialized with the potential to transform. For a material, one aspect of recursive hierarchical geometry was recently discussed for applications in flexible electronics (22). Here, by analogy to the stem cell, we demonstrate that starting from a simpl...
