This work focuses on creating novel structures by combining elements of common origami patterns. Multiple different types of physical and computer models are implemented to represent and analyze the structures. These structures have a broad range of potential applications, such as architecture, soft robotics, and aerospace. A combined Miura and EggBox pattern is presented. The combined unit cell for the sheet is parameterized, the Poisson ratio is calculated, and the sheets are 3D modeled using Solid Edge. Tubes constructed from the combined pattern are computer modeled and a static analysis is performed using the MERLIN2 software package in GNU Octave. These tubes can then be woven into cellular structures, some examples of which are 3D modeled and discussed. Also presented are many different combinations of the Miura and Resch unit cells. Crease patterns were drawn in Inkscape and computer folded using Origami Simulator. Some of these tessellations were found in literature but others were not. In addition to traditional origami paper folding, other fabrication methods for folded structures are presented, such as selective laser sintering (SLS) 3D printing and laser cutting of plastic sheets. Some software tools were developed and implemented to aid design.