Design of isomorphic symmetric descendants of the Miura-ori

Abstract

The Miura-ori is a classic flat-foldable tessellation which has its root in origami, but has been applied to the folding of reconfigurable structures for a variety of engineering and architectural applications. In recent years, researchers have introduced design variations on the Miura-ori which change both the form and the function of the pattern. This paper introduces the family of isomorphically generalized symmetric variations of the Miura-ori. We study the Miura crease pattern as a wallpaper pattern. We reduce the symmetry of the original crease pattern to design new patterns while at the same time preserving the symmetry group of the tessellation as well as the flat-foldability condition at each node. It will be shown that—through appropriate design variations on the original pattern—we are able to use the Miura-ori to design either globally planar, or globally curved, flat-foldable patterns.