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\subsection{Kinetic Wulff Plot}  We use the methods described in \cite{Zhang_2006} to construct the kinetic Wulff plot. The NC shape is defined to contain six {100} faces and eight {111} faces. Each variation of the NC shapes will have different relative sizes of the {100} and {111} faces. This allows the shapes to range from octahedron to cubes with intermediates as various truncation of cubo-octahedra. How the growth kinetics of each faces influences the NC shapes is described bythe systems of ODEs in the form  \begin{equation}  \label{eqn:model-wulff}  \frac{dx_i}{d \xi} = R_i - x_i \qquad i = 1, \dots, N-1  \end{equation}  where $x_i$ is the dimensionless perpendicular distance of face $i$ from the shape center, $\xi$ is the dimensionless time, $R_i$ is the relative growth rate of face $i$, and $N$ is the number of faces. When the relative growth rates are constant, it has a unique and stable steady state solution of  \begin{equation}  \label{eqn:soln-wulff}  x_i = R_i \qquad i = 1, \dots, N-1.  \end{equation}  The steady state solution where $x_i$ is the dimensionless perpendicular distance of face $i$ from the shape center, $R_i$ is the relative growth rate of face $i$, and $N$ is the number of faces. Eqn. \ref{eqn:soln-wulff}  is used to construct the kinetic Wulff plot by varying the relative growth rates. The shape calculation procedure can be summarized as following: \begin{enumerate}  \item From the defined relative growth rates, calculate the perpendicular distance $x_i$ of each face.  \item Extend the plane of each face at the perpendicular distance from the shape center until it coincides with adjacent planes.