# Different Configurations of the Non-Minimal Prismatic Tensegrities
## 1 Introduction
They are classified as \"abstract tensegrities\", since the bars of each layer are not connected to each other (\(T\), \(S\), \(C\), \(M\), \(D\) and \(I\)). From the point of view of an observer, the precise classification is less important than the architectural beauty. From the structural engineering point of view, the stiffness and economy are crucial. Therefore, the search for more stiff static schemes is driving this research, emphasizing the need to preserve the look-a-like tensegrity forms. Consequently, an analysis on non-minimal prisms is performed here. It is worth noting that some other tensegrity structures were raised; however, these are not prismatic ones. The most impressive are the Olympic Gymnastic Hall is Seoul ([PERSON] dome) or the Atlanta Stadium Georgia Dome ([PERSON] dome) [56]. Others are the Blur Building in Switzerland [57] and Kurilpa Bridge in Australia [58]. Some other tensegrity concepts were also considered, such as the Tor Vergata Footbridge [59] or the deployable footbridge [60]. In comparison to minimal prismatic systems, studies on non-minimal prismatic tensegrities are scarce. In general, non-minimal prismatic \(t\)-strut tensegrities in their most basic form are understood as prismatic ones with an additional number of \(t\) cross cables--see the modification between Figure 1b,e. It is well known that additional cables eliminate the infinitesimal mechanisms and stiffen the structure. Also, that is why \"pure or abstract tensegrities\" become \"structures with tensegrity features\", as was presented in terms of classification. The most complete survey on these basic non-minimal prismatic tensegrities was performed by [61], where prisms of up to seven bars were studied. A procedure called \"reconfiguration\" was performed--see [62]. In the reconfiguration, the minimal prism is firstly prestressed, then additional cables are attached and afterwards these cables are shortened, creating the non-minimal prism and further prestressing the system. Also, studies on modifications with more additional members were performed. In [63], analyses on different kinds of prismatic tensegrities, with additional cable nets, were performed for space deployable constructions. In [64], a generalized form of prismatic tensegrities, called dihedral-line tensegrity structures, was presented. Also, in [65] three new prismatic tensegrities were created by modifying the three-bar prism by creating specific connections between existing and additional cables. Please note that the existing literature always assumes that additional members are cables (see Figure 1e or Figure 2b for non-minimal triplex). Moreover, it assumes that the angle of rotation between the upper and lower bases \(\alpha\) does not change. The novelty of this study shows that there are other configurations, which possess a doubled number of bars. For example, Figure 3a presents a minimal quartex prism, which possesses four bars in its basic form. Typically, a non-minimal quartex is understood as the modification of the previous one in which additional cables are mounted--see Figure 3b. Please note that these members are called cables, yet in the prestressed configuration they carry zero internal forces. In both cases the angle of the rotation between the upper and lower bases, here denoted as \(\alpha\), is equal to 135 degrees. What was not reported in the literature is that if the number of members is non-minimal, other values of the angle of rotation \(\alpha\) are also possible and also create a stable configuration. For example, Figure 3c presents a non-minimal quartex with an angle \(\alpha\) equal to 130 degrees, and Figure 3d presents a non-minimal quartex with an angle \(\alpha\) equal to 110 degrees--both are stable. These configurations possess eight bars, instead of four. Therefore, it is shown that additional members can serve as bars, as well as that other angles of rotation \(\alpha\) are possible to obtain.