# Tensegrity Applications to Architecture, Engineering and Robotics: A Review
## 2 Applications for AEC
### Domes and Roofs
The structure is a vaulted dome composed of interconnected detachable and deployable four square-based tensegrity units. Probably, these DLTGs are the most promising tensegrity configurations for architectural roofing. These are composed of tensegrity units that form double-layer cable nets held apart by a set of disconnected rigid members. DLTGs were used again by [PERSON] et al. [46] to build different types of roofs. The first example (Figure 10a) shows a patio roof for a bank annex in Greece, composed of 4T-Prisms (2007) and the second one (Figure 10b) shows an Information Pavilion for \"Patras Cultural Capital of Europe\" in Greece, made also by the juxtaposition of 4T-Prism or Simplex (2006). Figure 7: (**a**) Prototype of a knit tensegrity shell with membrane and bamboo struts. Reprinted with permission from Ref. [41]. (**b**) Tensegrity canopy composed by expanded cuboctahedrons Reprinted with permission from Ref. [42]. Figure 8: Tensegrity structures by [PERSON] (images taken from [43]): (**a**) Entrance canopy in Diemen. (**b**) Support of triangular truss bridge in Amsterdam. (**c**) Tensile structure in the Amsterdam Maritime Museum. (**d**) Hemweg canopy in Amsterdam. Figure 9: (**a**) [PERSON] working in his studio in 1961 with a DLTG (Illustration donated by the artist). (**b**) “Semi-Open Exhibit Space”: Entry for the international competition on the design of “Ephemeral Structure for the City of Patras” [45] (Image courtesy of [PERSON]). One of the main advantages of this type of structures is the foldability. In 2014, [PERSON] et al., built a Deployable DLTG (DDLTG) composed of Quastruts [47] (Figure 11). When some of the continuous wires were released, it was possible to fold the whole structure (originally 16 m\({}^{2}\)) to a folded configuration with a perimeter less than 1.80 m, being contained in a cylinder of 0.28 m radius and 1.70 m height. The structure could be easily stored, transported and erected quickly and easily, allowing it to be used as a temporary shelter, exhibition roof structure, etc. At Tokyo University, [PERSON] et al. [48] built two tensegrity skeletons to support a membrane roof that covers the White Rhino (Figure 12). The tensegrity structures were built from the so-called 'Simplex' tensegrity, composed of three struts and nine strings. These units have one infinitesimal inextensional displacement mode, a twisting motion between the upper and lower triangles, in which the frame exhibits extremely low rigidity. Thus, there were added three more tendons between six unconnected points of Simplex in order to increase its structural rigidity drastically. Additionally, the frame was completed with a set of three suspension tendons supporting an isolated vertical strut that maintains the membrane roof and transmits its external loads to the tensegrity frame. Figure 11: DDLTG 4 \(\times\) 4 m\({}^{2}\) in its unfolded (**a**) and folded (**b**) configurations. Lower inner nodes are numbered in red and nodes of the lower boundary are numbered in cyan. Figure 10: Applications of Double-Layer Tensegrity Grids: (**a**) Patio roof in Greece; (**b**) Exhibition Pavilion in Patras (Greece), both by [PERSON] [46]. (Images courtesy of [PERSON]). Recent studies on the matter conducted by [PERSON] et al. [49] have proposed a wave-curved tensegrity dome which provides more options for architectural design. Another hybrid cable dome, among many others, was suggested by [PERSON] et al. [50], where they replaced the conventional concrete ring with a flexible tensegrity torus. Even though both proposals are just structural designs and have not been applied to real constructions yet, it is a signal that there are still some research groups pushing the boundaries of tensegrity applications for domes and roofs.