  Origami-based mechanical metamaterials have recently received significant
scientific interest due to their versatile and reconfigurable architectures.
However, it is often challenging to account for all possible geometrical
configurations of the origami assembly when each origami cell can take multiple
phases. Here, we investigate the reconfigurability of a tessellation of
origami-based cellular structures composed of bellows-like unit cells,
specifically Tachi-Miura Polyhedron (TMP). One of the unique features of the
TMP is that a single cell can take four different phases in a rigid foldable
manner. Therefore, the TMP tessellation can achieve various shapes out of one
originally given assembly. To assess the geometrical validity of the
astronomical number of origami phase combinations, we build a graph-theoretical
framework to describe the connectivity of unit cells and to analyze the
reconfigurability of the tessellations. Our approach can pave the way to
develop a systematic computational tool to design origami-based mechanical
metamaterials with tailored properties.
