## 2 Materials and Methods
### Data Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Factors** & & & **Responses** \\ \hline \multicolumn{2}{c}{**Cell Type (CT)**} & **Lattice Thickness (T), mm** & **Cell Size (X), mm\({}^{3}\)** & **SA/V\({}_{\rm S}\)** & \(\Delta\)T = T\({}_{\rm T}-10^{\circ}\)**C** \\ \hline \multirow{7}{*}{1} & Gyroid & Thin: 1.5 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 1.9 & 2.2 \\  & Gyroid & Thin: 1.5 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.9 & 2.2 \\  & Gyroid & Thin: 1.5 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 1.8 & 2.1 \\  & Gyroid & Moderate: 2 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 1.5 & 1.7 \\  & Gyroid & Moderate: 2 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.5 & 1.7 \\  & Gyroid & Moderate: 2 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 1.5 & 1.7 \\  & Gyroid & Thick: 4 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 0.7 & 0.7 \\  & Gyroid & Thick: 4 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 0.8 & 0.9 \\  & Gyroid & Thick: 4 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 0.9 & 0.9 \\ \hline \multirow{7}{*}{2} & Diamond & Thin: 1.5 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 2.0 & 2 \\  & Diamond & Thin: 1.5 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.9 & 2.1 \\  & Diamond & Thin: 1.5 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 1.9 & 2.2 \\  & Diamond & Moderate: 2 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 1.5 & 1.6 \\  & Diamond & Moderate: 2 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.5 & 1.6 \\  & Diamond & Moderate: 2 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 1.5 & 1.6 \\  & Diamond & Thick: 4 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 0.6 & 0.6 \\  & Diamond & Thick: 4 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 0.8 & 0.8 \\  & Diamond & Thick: 4 mm & Large: 20 \(\times\) 20 \(\times\) 20 & 0.8 & 0.8 \\ \hline \multirow{7}{*}{3} & Lidinoid & Thin: 1.5 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 1.9 & 1.2 \\  & Lidinoid & Thin: 1.5 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.8 & 1.2 \\  & Lidinoid & Thin: 1.5 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 1.8 & 1.4 \\  & Lidinoid & Moderate: 2 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.4 & 1 \\  & Lidinoid & Moderate: 2 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 1.4 & 1.1 \\  & Lidinoid & Thick: 4 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 0.6 & 0.5 \\  & Lidinoid & Thick: 4 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 0.8 & 0.6 \\  & Lidinoid & Thick: 4 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 0.8 & 0.6 \\ \hline \multirow{7}{*}{4} & SplitP & Thin: 1.5 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 2.3 & 2.3 \\  & SplitP & Thin: 1.5 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 2.2 & 2.5 \\  & SplitP & Thin: 1.5 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 2.3 & 2.5 \\  & SplitP & Moderate: 2 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 1.7 & 1.6 \\  & SplitP & Moderate: 2 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 1.8 & 1.8 \\  & SplitP & Moderate: 2 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 1.8 & 1.9 \\  & SplitP & Thick: 4 mm & Small: 12 \(\times\) 12 \(\times\) 12 & 0.6 & 0.4 \\  & SplitP & Thick: 4 mm & Medium: 16 \(\times\) 16 \(\times\) 16 & 0.8 & 0.8 \\  & SplitP & Thick: 4 mm & Large: 18 \(\times\) 18 \(\times\) 18 & 0.9 & 0.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Design table of the three level factors and responses for each cell type. The regression model is developed to find the regression equations using the following guide from Minitab [49]. To design the model, two factors (T and X) with three levels (T: Thin, Moderate, Thick; X: Small, Medium, Large) and two responses are used. Pareto charts of the standardized effects help to visualize the effects of the factors on the responses. Other parameters such as model summary, residual plots, and table of analysis of variance are automatically produced by Minitab as supplementary information to the statistical models. Then response optimization is conducted to achieve the multi-objective goals for this study following the Minitab guide [50].