Deployable structures can transform and/or expand and contract due to their geometrical, material and mechanical properties. This technology enables an architecture that can be transportable, mobile, adaptable, rapidly built, reusable and that makes efficient use of space and materials and therefore embraces the concept of sustainability. Currently, a wide range of deployable structures are being generated by different disciplines, in many different types of materials and that can vary hugely in scale and application. This is a relatively new field of research, and contemporary literature is made mostly of dislocated studies, where one by one, a new structure is developed, without an understanding of how different deployable structures relate to one another. While contemporary research has placed a lot of emphasis on structural efficiency, material properties and actuators, this research focuses on their geometry in order to generate a comprehensive understanding that can also lead to architectural innovation. This research proposes that different deployable structures can share common geometric properties. By carrying out an analysis of scissor-hinged case studies, this research has created a visual framework that explains the geometry of these structures. This visual framework illustrates how the scissor hinged case studies have gradually evolved over time, increasing in complexity. This understanding has led to the creation of several geometric methods for scissor hinged deployable structures as well as thick origami that have generated architectural innovation as demonstrated by the case studies and built prototypes, therefore increasing our knowledge of what can be achieved with this technology. The research outcomes also challenge the categorical approach towards the understanding of different types of deployable structures, in particular through the creation of a new hybrid type of deployable structure: Origami-Scissor hinged. The significance in expanding the knowledge of what it is possible to achieve with deployable structures reverberates throughout multiple disciplines and exists at the very intersection of science and art. As well as exemplifying a sustainable emerging technology for architecture, deployable structures are being included in books of history of art in various educational centres in the world. These are also reusable and light structures that contribute to science and society in different dimensions: in a world constantly in change, they can provide accommodation in transitional stages of migrations and natural disasters, they can create adaptable environments and rapid construction strategies in permanent architecture, they can be used in stage design for entertainment. Deployable structures are also used in the International Space Station for space architecture; they are also used for satellites that facilitate world communication and for solar arrays that gather energy from the Sun. Therefore, to expand our knowledge of what is possible to achieve with deployable structures can significantly contribute to architecture on Earth and in space, as well as the complex multidisciplinary fields with which the subject engages.