Variable-geometry structures are useful in aerospace applications because they are deployable, from a compact configuration (launch phase) to a spread geometry (operational phase). They may also benefit from the use of flexible joints, which store elastic energy for automatic deployment. Following the development of a self-deploying antenna frame structure with scissors, the geometrical configuration of a new kind of structure, simpler, lighter, and minimizing mechanical joints between elements, is proposed in this article. This topology can form a three-dimensional structure when partially opened or a planar structure when fully deployed. The applications concern autotensioning structures such as meshed space antenna, deorbiting sails, and also solar panel support structures.