Now we investigate how the loading capabilities between the two configurations differ. To answer this question, we first analyze the breadth (\(B\)) change of the TMP unit cell as a function of \(\gamma\) for the two different $\alpha$ angles: \(45\degree\) and \(70\degree\) as shown in Figure \ref{714806}a. Here, \(B\) is normalized by the value at \(\gamma=1\). The case of \(\alpha=45^{\circ}\) shows that \(B\)increases monotonically as \(\gamma\) increases, and the structure takes its maximum value at \(\gamma=1\). On the other hand, the TMP with \(\alpha=70^{\circ}\) exhibits the non-monotonic change of \(B\), and it reaches the maximum breadth at the critical folding ratio, \(\gamma_C=0.28\).
It is this non-monotonic shape of \(B\) that endows both collapsible and load-bearing capabilities of the TMP. That is, if we apply compression to the TMP along the 2-axis (i.e., decreasing \(B\)), the structure will collapse when the initial configuration of the TMP is positioned on the left side of the critical point (marked by (i) in Figure \ref{714806}a). However, if the initial posture of the TMP is on the right side of the critical point (case (ii) in Figure \ref{714806}a), the structure will deform in a way that its breadth is maintained kinematically, which leads to the load-bearing capability under assumption of rigid origami.
It is notable that the choice of this mechanical bifurcation between collapsible and load-bearing modes is determined by the initial posture of the TMP, without necessitating the manipulation of its crease patterns. We also observe from the inset illustrations in Figure \ref{714806}a that the cross-section of the collapsible mode shows a convex shape, whereas the load-bearing configuration exhibits a concave shape. The close relationship between the TMP's auxetic and load-bearing properties is discussed in \textit{SI Appendix} (Fig. S2 and section S2 for more details).