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\section{Kinetic Wulff Plot}  Away from equilibrium, the NC shape is governed by the kinetics of inter- and intrafacet atom diffusion, as well as by the kinetics of deposition to various facets. At nonequilibrium growth conditions, the resulting shapes are expected to be different from the thermodynamic shapes. Examples of well-known kinetic shapes are rod-like and highly branched (bi- and tripods) structures \cite{Xiong_2007}. When NCs grow beyond a critical size, the relative atom deposition rate to various facets becomes a major influence in the NC shape. In this kinetically-controlled growth regime, the kinetic Wulff construction can predict the shape evolution of faceted crystal growth based on the surface kinetics \cite{Du_2005,frank1958growth,osher1997wulff}. Using 3-dimensional shape evolution calculation method \cite{Zhang_2006}, we correlate the relative flux of deposition to \{111\} and \{100\} facets $\frac{F_{111}}{F_{100}}$ and the resulting kinetic Wulff shape in the reversible octahedron-to-cube transformation. This transformation is observed in the seed-mediated growth of Ag NCs \cite{Xia_2012}, in which the shape-controlling knob is concentration of poly(vinylpyrrolidone) in the solution. The constructed kinetic Wulff plot is shown in Figure 1, which maps the predicted shape as a function of the relative atom flux $\frac{F_{111}}{F_{100}}$. The method of how the kinetic Wulff plot was constructed is described in the supporting information. When the relative flux to \{111\} facets is less than half of the flux to \{100\} facets, the octahedra is predicted as the kinetic Wulff shape. As $F_{111}$ increases relative to $F_{100}$, we observe a shape progression from octahedra to cubo-octahedra, then to truncated cubes, and eventually to cubes at $\frac{F_{111}}{F_{100}} \geq \sqrt{3}$.  In this work, we choose the seed-mediated Ag polyol synthesis with PVP as the model and use large-scale MD simulations to quantify $F_{100}$ and $F_{111}$ and construct kinetic Wulff shape plot to probe the cube-to-octahedron transformation. Our study reveals the mechanism by which SDAs impart shape selectivity.