In its simplest form, the invention is an array of 10 triangles arranged in a specific pattern. When arranged in this pattern, these triangles interact in a unique way, such that a new useful three-dimensional shape emerges. When this pattern of triangles is applied to any flat material, either through folding, impressing, affixation of hinges, or some other method, the formerly flat material can be manipulated to become a durable, three-dimensional hinged appendage.