The variable-geometry structures are useful in the aerospace applications because they cross of a compact configuration (launch phase) in a spread geometry (operational phase). Due to its expertise on the conception of light weight structures, the SIGECO team designs and realizes innovative structures: their advantage is to deploy automatically by storage of energy of flexion in flexible joints. A first study was led on a structure with scissors which conceive the skeleton of an auto-deployable satellite antenna. Following upon these works, the aim of this article is to propose the geometrical configuration of another kind of structure without articulations between elements (pivots, slide junctions). This structure form a circular plane or a three-dimensional structure (partially opened). The bar number is divided by two compared to the scissor. The applications concern auto-tensing structures as space antenna (LDR or other), desorbitation or solar sails and stiff structures for the support of solar panels.