As novel engineered materials, metamaterials have properties that are not found in naturally occurring materials. These unique mechanical and/or electromagnetic properties are different from the properties of naturally occurring singlecrystalline materials such as 2D transition metal compounds (e.g., metal selenides and halides [1] ) and can be realized using assemblies of multiple composite materials such as metals and plastics. Some examples of these materials are hypertonicity materials with directional propagation of light within and on the material surface, [2] electromagnetic bandgap materials, [3,4] bi-isotropic and bianisotropic electromagnetic materials, [5,6] and mechanical cellular materials [7] with low density, high mechanical strength, [8] significant damping, damage tolerance, [9] and negative Poisson's ratio (PR). [10] Due to their advanced engineered properties, metamaterials can potentially enable many improved engineering products and applications such as high-performance antennas, acoustic control, and structural stability enhancement [11,12] that cannot be realized using naturally existing materials. In particular, auxetic materials display negative PR during tension/compression and can be used to increase the shear modulus, [13] damping effect, sound bandwidth control, [14] structural flexibility, [15,16] and energy absorption effect. [17,18] Their special enhancement effects make them useful for structural protection, [19] wearing comfort, sensing, fastening, and sealing applications. [11] It is clear that the positive/negative thermal expansion coefficient [20] and positive/ negative PR [21] in the same origami pattern are related during the material deformation under temperature variation. Solid materials with a tunable PR are desirable for engineering applications including tunable acoustics, vibration control, and soft robotics. [22] Previous studies have developed different forms of 2D and 3D metamaterials such as dichalcogenides, [23] foams, [24] and origami structures, [21,25] with a large tuning range of negative PR [23] and high average recoverability from compression by more than 30%. [26] For biomedical applications, tissue engineering scaffolds with positive/negative PR can be tailored to match the attributes of the target tissue [27,28] and give rise to deformations that are synchronized with the beating of the heart. [29] Recently, a design framework integrating topology optimization, parametric design, and compression was developed for the gradually stiffer mechanical metamaterials. [30] Many designs have been proposed to realize auxetic cellular materials, [11] such as 2D re-entrant honeycombs composite, [1,31,32]