# Tensegrity Applications to Architecture, Engineering and Robotics: A Review
## 2 Applications for AEC
### Domes and Roofs  
Several tensegrity-based domes have been proposed throughout the tensegrity history. This is probably because it is simple to obtain a sphere from a polyhedral tensegrity structure such as a regular dodecahedron or icosahedron. Probably the first examples of this kind of tensegrity structure were the two tensegrity domes constructed by [PERSON] in 1953 in Princeton University and University of Minnesota [30]. The former was a 40-foot-diameter 90-strut tensegrity enenticontahedron and the latter was a 40-foot-diameter 270-strut tensegrity hemisphere (Figure 3a). Even if it was a milestone in tensegrity history, it lacked stability due to the absence of triangulation in the connecting cables. Therefore, the application of tensegrity domes to architecture was not successful at that stage. [PERSON] also developed and patented the so-called Aspenison Dome (Figure 3b), [31]. The design was based on the one of a bicycle wheel, preconizing a specific type of structure called cable dome, in which the radial cables connect an outer compression ring to an inner tension ring. As he explains in his patent:  
_\"... a catenary suspension system can be converted into an arched structure of domical or polygonal form. By breaking up the suspension cables into increments suspending an ascending series of polygonal or circular frames stepped upwardly one within another, altitude is gained, replacing the catenary sag of the bridge cables with a rising, arched, suspension system\"_[31]. The Aspenison Dome was used as an inspiration for the Olympic Fencing and Gymnastic Arena in Seoul (Republic of Korea) (Figure 4a). This stadium's roof was built by [PERSON] in 1988. The radial cables connecting the inner and the outer ring in [PERSON]'s design formed triangles, whereas in [PERSON]'s design, these belong to vertical planes passing through the central symmetry axis of the whole structure. Figure 3: (a) Tensegrity Dome by [PERSON] at the University of Minessota, 1953 (photo from [30]). (b) Top and front view of [PERSON]’s Aspenison Dome (photo from [32]). These two examples, as well as others inspired by [PERSON]'s works [36], belong to the category of the cable dome, which has been widely used along the last 5 decades [36; 37]. However, the cable dome does not fully participate in the tensegrity principle because it can only work in co-function with an outer compressed ring beam to form a truly self-stressed, self-equilibrium system [38]. Some authors do not consider them real tensegrity systems because the boundary is delimited by a compressed element (the peripheral concrete beam), instead of components in tension (wires, tendons or membranes). Based on these ideas of domes, some tensegrity roofs have been built over the last years. One example is the Stadium of the City of La Plata [34] designed in the late 1990s (Figure 4b). This roof was built from a tensegrity system entailing four elements: a cable net forming triangles, triangulated cables in suspension, hoop cables, and rigid vertical posts. The La Plata design is an application of the patented tensegrity structure system first developed for use at the Georgia Dome in Atlanta (Figure 4c). In fact, the structural engineers were Weidlinger Associates, who also worked on the analysis of this dome. However, as already said, these kinds of roofs cannot be considered pure tensegrity roofs due to the metallic external ring (in compression) that supports the structure. Something similar happens with the World Cycling Centre in Aigle in (Switzerland) (Figure 4d) designed by [PERSON] and [PERSON] [35]. The cycling track has a 200 m length and it is dimensioned to receive 700 people. The roof is built upon a pneumatic membrane, an elliptical ring surrounding the structure and an inner bi-pyramidal tensegrity structure. Figure 4: (**a**) [PERSON]’s 1988 Olympic Arena in Seoul (photo from [33]).