A Framework for the Symmetric Generalisation of the Miura-ori

Abstract

The Miura fold pattern, or the Miura-ori, is a flat-foldable origami tessellation which has been applied to the folding of deployable structures for various engineering and architectural applications. In recent years, researchers have proposed systematic (see, e.g., [1] or [2]), and also free-form [3], variations on the Miura pattern. This paper develops a geometric framework for the symmetric generalisation of the Miura-ori while preserving the ‘stacking while folding’ behaviour of the pattern. We present a number of novel concepts and definitions which help us apply systematic variations on the original pattern. We study the Miura crease pattern as a pmg wallpaper pattern which is one of the seventeen distinct wallpaper groups. We reduce the symmetry of the Miura-ori to obtain new patterns while preserving the flat-foldability condition at each node. We conclude that we are able to use the Miura-ori, which is a globally planar pattern in its partially folded states, to systematically design either ‘globally planar’ or ‘globally curved’ patterns, through appropriate design variations on the original pattern.