Inspired by the concept of origami, a design methodology of extremal metamaterial is developed and the effective elastic tensors of the metamaterials are obtained. Different soft modes are realized with special line-plane connections between the cubes and hexahedrons of an origami unit and the transition from nullmode to hexamode is also demonstrated. A new pentamode metamaterial with only one resistant deformation that is not hydrostatic is designed. By further degrading the local connections, a hexamode metamaterial is realized for the first time. It is believed that the design methodology can unlock a new field of extremal metamaterials with novel properties.
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