The Miura fold pattern, or the Miura-ori, is a flat-foldable origami tessellation with a wide range of engineering applications. In particular, the Miura-ori has been applied to the folding of deployable structures for various architectural applications, e.g. folding roofs and shelters. In recent years, researchers have proposed variations on the Miura-ori which change both geometry and functionality of the pattern.We introduce a framework for the symmetric generalisation of the Miura-ori. We study the Miura crease pattern as a "pmg" wallpaper pattern. 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 to systematically design a variety of novel patterns, through appropriate design variations on the original pattern.