The boundary between the colored and white zones can be calculated numerically by solving Eq.~\ref{eq:critical_angle}. % \hl{by putting $\gamma_C = 1$}. % (i.e., $\theta_M = 0 and \theta_G = 2\alpha based on Eq. ).
The result is shown in the solid black curve in Fig.~\ref{fig:Kinematics}\textit{B}.
In the case of $d/m=0.75$, the boundary is formed at $\alpha = 57^{\circ}$ (see the crossing between the black curve and the vertical dashed line in Fig.~\ref{fig:Kinematics}\textit{B}). %This is based on the analysis of a single TMP unit cell under the condition of $l = m$.
Note in passing that if we consider an infinite chain of TMP unit cells stacked in the 2-axis, this boundary approaches $\alpha=45^\circ$ regardless of the length ratio (see \textit{SI Appendix}, section S3 for more details). We also find that not all parameters considered in this design space produce a realistic TMP structure. In Fig.~\ref{fig:Kinematics}\textit{B}, the gray colored area represents a forbidden design space, where the collision between the side facets happens (see the upper right inset in Fig.~\ref{fig:Kinematics}\textit{B}). Mathematically, this self-intersection can be avoided if $2l - d\cot(\alpha) + 2m\cos(2\alpha) > 0$~\cite{Yasuda2015}, and this boundary (upper black curve) is shown in Fig.~\ref{fig:Kinematics}\textit{B}.