  The Japanese art of turning flat sheets into 3D intricate structures,
origami, has inspired design of mechanical metamaterials. Mechanical
metamaterials are artificially engineered materials with uncommon properties.
Miura-ori is a remarkable origami folding pattern with metamaterial properties
and a wide range of applications. In this study, by dislocating the zigzag
strips of a Miura-ori pattern along the joining ridges, we create a class of
one-degree of freedom (DOF) cellular mechanical metamaterials. The resulting
configurations are based on a unit cell in which two zigzag strips surround a
hole with a parallelogram cross section. We show that dislocating zigzag strips
of the Miura-ori along the joining ridges, preserves and/or tunes the
outstanding properties of the Miura-ori. The introduced materials are lighter
than their corresponding Miura-ori sheets due to the presence of holes in the
patterns. Moreover, they are amenable to similar modifications available for
Miura-ori which make them appropriate for a wide range of applications.
