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A novel origami cellular material based on a deployable cellular origami structure is described. The structure is bi-directionally flat-foldable in two orthogonal (x and y) directions and is relatively stiff in the third orthogonal (z) direction. While such mechanical orthotropicity is well known in cellular materials with extruded two dimensional geometry, the interleaved tube geometry presented here consists of two orthogonal axes of interleaved tubes with high interfacial surface area and relative volume that changes with fold-state. In addition, the foldability still allows for fabrication by a flat lamination process, similar to methods used for conventional expanded two dimensional cellular materials. This article presents the geometric characteristics of the structure together with corresponding kinematic and mechanical modeling, explaining the orthotropic elastic behavior of the structure with classical dimensional scaling …