# Different Configurations of the Non-Minimal Prismatic Tensegrities
## 4 Examples
### Pentex Module  
Based on presented equations, a prism with whichever number of struts can be analyzed. However, in order to retain drawings readable, the pentex (\(t=5\)) was chosen. The geometrical lengths are \(r_{\mathrm{g}}=500\) mm (\(l_{\mathrm{g}}=587.79\) mm) and \(b_{\mathrm{g}}=2000\) mm, and the dependent lengths are \(s_{\mathrm{g}}=1847.22\) mm and \(a_{\mathrm{g}}=1797.38\) mm. The structure's geometrical height is \(h_{\mathrm{g}}=1790.56\) mm. The assumed product \(E_{\mathrm{s}}A_{\mathrm{s}}=E_{\mathrm{b}}A_{\mathrm{b}}=E_{\mathrm{f}}A_{ \mathrm{l}}=E_{\mathrm{a}}A_{\mathrm{a}}=10^{3}\) N results in stiffnesses equal to \(k_{\mathrm{s}}=0.5414\) N/mm, \(k_{\mathrm{b}}=0.5\) N/mm, \(k_{\mathrm{a}}=0.5564\) N/mm and \(k_{\mathrm{l}}=1.7013\) N/mm. Please note that here stiffnesses are calculated based on geometrical lengths, whereas in numerical calculations they are referred properly to the natural lengths.  
The module is prestressed based on scenarios presented in Table 4. In scenarios 1-3, cross cables, bars and horizontal cables are the cause of the prestress, respectively. In scenarios 4-5, the additional members are the cause of the prestress. Please note that using the prestressing coefficients, changes in multiple groups of members can be the cause of prestress, yet no such scenario was shown here. The results are given in Table 5 and Figure 13.  
Again, one obtains a ten- or five-bar structure. If the sign of the rotational angle \(\theta\) is positive, one obtains the five-bar prism (scenarios 2, 3 and 4--please note values of forces in additional members in Table 4). If the \(\theta\) sign is negative, one obtains a ten-bar prism (scenarios 1 and 5). In general, it can be concluded that shortening the additional members and horizontal cables, as well as lengthening the bars, creates a \(t\)-bar non-minimal prism, while shortening the cross cables and lengthening the additional members creates a \(2t\)-bar non-minimal prism. Also, it is clear that prestressing by changing the lengths of additional  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & \\ \hline Prestressing coefficients & \(1\) & \(2\) & \(3\) & \(4\) & \(5\) \\ \hline \(c_{\mathrm{s}}\) (-) & \(0.98\) & \(1.0\) & \(1.0\) & \(1.0\) & \(1.0\) \\ \hline \(c_{\mathrm{b}}\) (-) & \(1.0\) & \(1.02\) & \(1.0\) & \(1.0\) & \(1.0\) \\ \hline \(c_{\mathrm{a}}\) (-) & \(1.0\) & \(1.0\) & \(1.0\) & \(0.98\) & \(1.02\) \\ \hline \(c_{\mathrm{l}}\) (-) & \(1.0\) & \(1.0\) & \(0.98\) & \(1.0\) & \(1.0\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Prestressing scenarios.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **1** & **2** & **3** & **4** & **5** \\ \hline \(\theta\) (deg) & \(-6.69\) & \(5.88\) & \(1.80\) & \(14.22\) & \(-12.27\) \\ \hline \(r\) (mm) & \(501.13\) & \(501.50\) & \(490.20\) & \(500.20\) & \(500.10\) \\ \hline \(b\) (mm) &  
members causes the prism to rotate significantly in comparison to prestressing by changing in the lengths of other groups.  
Again, the presented non-minimal pentex is classified as a \"structure with tensegrity features\", regardless of whether it is built from ten or five struts.