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%%
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\author{M.~Akhtar}
\author{T.~Coates}
\author{S.~Galkin}
\author{A.M. Kasprzyk}
\title{Minkowski Polynomials and Mutations: Appendices}
\begin{document}
\vspace{-1.5cm}
%\maketitle

\centerline{\Huge \bf Minkowski Polynomials and Mutations: Appendices}
\vspace{2.5mm}

\centerline{\Large \bf Mohammad AKHTAR, Tom COATES, Sergey GALKIN and  Alexander M.~KASPRZYK}

\setcounter{page}{18}

\vspace{3mm}

This document contains the Appendices to the paper \textit{SIGMA} \textbf{8} (2012), 094, 707~pages, \href{http://dx.doi.org/10.3842/SIGMA.2012.094}{http://dx.doi.org/10.3842/SIGMA.2012.094}

\vspace{2mm}

\appendix

\pdfbookmark[1]{Appendix A: Minkowski Period Sequences}{AppendixA}
\begin{center}
  {\Large \bf Appendix A: Minkowski Period Sequences}
  \end{center}

\vspace{-1mm}

\setcounter{table}{-1}

\begin{table}[!h]
  \caption{IDs for Minkowski period sequences.  The period sequences are sorted
    lexicographically.}

    \vspace{-2mm}
  \tiny
  \centering
    \vspace{3ex}
  \begin{tabular}{lr@{\hspace{9ex}}lr@{\hspace{9ex}}lr@{\hspace{9ex}}lr}
  \toprule
  \multicolumn{1}{c}{Period sequence} &
  ID &
  \multicolumn{1}{c}{Period sequence} &
  ID &
  \multicolumn{1}{c}{Period sequence} &
  ID &
  \multicolumn{1}{c}{Period sequence} &
  ID \\
  \cmidrule(r{2.5em}){1-2}
  \cmidrule(r{2.5em}){3-4}
  \cmidrule(r{2.5em}){5-6}
  \cmidrule(r{0em}){7-8}
1, 0, 0, 0, 24, 0, 0, 0, 2520, 0, 0,\ldots & 1 & 1, 0, 4, 24, 60, 720, 3640, 21840,\ldots & 43 & 1, 0, 8, 30, 240, 1740, 13130,\ldots & 85 & 1, 0, 20, 96, 1236, 11100, 122240,\ldots & 127 \\
1, 0, 0, 6, 24, 0, 90, 1260, 2520,\ldots & 2 & 1, 0, 4, 24, 132, 780, 5800, 40320,\ldots & 44 & 1, 0, 8, 30, 240, 1920, 13490,\ldots & 86 & 1, 0, 20, 96, 1428, 14160, 179120,\ldots & 128 \\
1, 0, 0, 12, 0, 0, 540, 0, 0, 33600,\ldots & 3 & 1, 0, 6, 0, 90, 0, 1860, 0, 44730, 0,\ldots & 45 & 1, 0, 8, 36, 288, 2220, 18260,\ldots & 87 & 1, 0, 20, 102, 1188, 11400, 117290,\ldots & 129 \\
1, 0, 0, 12, 24, 0, 540, 2520, 2520,\ldots & 4 & 1, 0, 6, 0, 114, 0, 2940, 0, 87570,\ldots & 46 & 1, 0, 10, 24, 318, 1680, 16300,\ldots & 88 & 1, 0, 20, 102, 1236, 11640, 125210,\ldots & 130 \\
1, 0, 0, 18, 24, 0, 1350, 3780, 2520,\ldots & 5 & 1, 0, 6, 6, 90, 180, 1950, 5460,\ldots & 47 & 1, 0, 10, 24, 366, 1800, 20620,\ldots & 89 & 1, 0, 20, 102, 1284, 12180, 136010,\ldots & 131 \\
1, 0, 2, 0, 6, 60, 20, 840, 70, 7560,\ldots & 6 & 1, 0, 6, 6, 90, 240, 1950, 8400,\ldots & 48 & 1, 0, 10, 30, 270, 1620, 11710,\ldots & 90 & 1, 0, 20, 108, 1284, 12720, 139340,\ldots & 132 \\
1, 0, 2, 0, 30, 0, 380, 0, 5950, 0,\ldots & 7 & 1, 0, 6, 6, 114, 240, 3030, 9660,\ldots & 49 & 1, 0, 10, 30, 270, 1860, 13510,\ldots & 91 & 1, 0, 20, 114, 1380, 14340, 164630,\ldots & 133 \\
1, 0, 2, 0, 30, 60, 380, 840, 5950,\ldots & 8 & 1, 0, 6, 12, 90, 360, 2040, 10500,\ldots & 50 & 1, 0, 10, 30, 294, 1620, 13150,\ldots & 92 & 1, 0, 20, 132, 1572, 18120, 221420,\ldots & 134 \\
1, 0, 2, 0, 54, 120, 740, 1680,\ldots & 9 & 1, 0, 6, 12, 90, 420, 2040, 12600,\ldots & 51 & 1, 0, 10, 30, 294, 1680, 13510,\ldots & 93 & 1, 0, 20, 132, 1812, 21720, 289100,\ldots & 135 \\
1, 0, 2, 6, 6, 120, 110, 1260, 5110,\ldots & 10 & 1, 0, 6, 12, 90, 420, 2040, 13020,\ldots & 52 & 1, 0, 10, 30, 318, 1740, 15310,\ldots & 94 & 1, 0, 22, 96, 1434, 12480, 148900,\ldots & 136 \\
1, 0, 2, 6, 30, 60, 470, 1680, 7630,\ldots & 11 & 1, 0, 6, 12, 90, 420, 2400, 13860,\ldots & 53 & 1, 0, 10, 30, 318, 2040, 17470,\ldots & 95 & 1, 0, 22, 108, 1530, 14760, 178240,\ldots & 137 \\
1, 0, 2, 6, 30, 120, 470, 2520,\ldots & 12 & 1, 0, 6, 12, 90, 480, 2400, 16800,\ldots & 54 & 1, 0, 10, 36, 270, 1980, 13240,\ldots & 96 & 1, 0, 22, 126, 1722, 18780, 236470,\ldots & 138 \\
1, 0, 2, 6, 54, 180, 830, 4620,\ldots & 13 & 1, 0, 6, 12, 114, 360, 3120, 12600,\ldots & 55 & 1, 0, 10, 36, 294, 2040, 15040,\ldots & 97 & 1, 0, 22, 174, 2514, 34200, 501070,\ldots & 139 \\
1, 0, 2, 12, 6, 120, 560, 840, 10150,\ldots & 14 & 1, 0, 6, 12, 114, 420, 3120, 15540,\ldots & 56 & 1, 0, 10, 36, 318, 2160, 17200,\ldots & 98 & 1, 0, 24, 0, 2520, 0, 369600, 0,\ldots & 140 \\
1, 0, 2, 12, 6, 180, 560, 1680,\ldots & 15 & 1, 0, 6, 12, 114, 480, 3480, 19320,\ldots & 57 & 1, 0, 10, 36, 366, 2640, 23320,\ldots & 99 & 1, 0, 24, 120, 1896, 19200, 255480,\ldots & 141 \\
1, 0, 2, 12, 30, 120, 920, 3360,\ldots & 16 & 1, 0, 6, 12, 114, 540, 3480, 22680,\ldots & 58 & 1, 0, 10, 42, 342, 2640, 21250,\ldots & 100 & 1, 0, 24, 156, 2280, 27960, 387060,\ldots & 142 \\
1, 0, 2, 12, 30, 180, 920, 4200,\ldots & 17 & 1, 0, 6, 12, 138, 480, 4560, 21840,\ldots & 59 & 1, 0, 10, 42, 414, 3300, 29890,\ldots & 101 & 1, 0, 24, 192, 2904, 40320, 611520,\ldots & 143 \\
1, 0, 2, 12, 54, 240, 1280, 7560,\ldots & 18 & 1, 0, 6, 12, 138, 540, 4200, 23520,\ldots & 60 & 1, 0, 10, 48, 390, 3240, 27820,\ldots & 102 & 1, 0, 26, 216, 3582, 54480, 874700,\ldots & 144 \\
1, 0, 2, 18, 30, 240, 1730, 5880,\ldots & 19 & 1, 0, 6, 18, 90, 540, 2850, 16380,\ldots & 61 & 1, 0, 10, 48, 438, 3720, 33940,\ldots & 103 & 1, 0, 28, 216, 3516, 49680, 783640,\ldots & 145 \\
1, 0, 2, 18, 54, 300, 2090, 10500,\ldots & 20 & 1, 0, 6, 18, 90, 600, 2850, 18900,\ldots & 62 & 1, 0, 10, 60, 510, 4920, 47080,\ldots & 104 & 1, 0, 32, 246, 4224, 61080, 998330,\ldots & 146 \\
1, 0, 2, 18, 102, 420, 2810, 21000,\ldots & 21 & 1, 0, 6, 18, 90, 660, 2850, 21840,\ldots & 63 & 1, 0, 10, 66, 558, 5400, 54010,\ldots & 105 & 1, 0, 32, 312, 5520, 91680, 1651640,\ldots & 147 \\
1, 0, 2, 36, 198, 840, 9200, 79800,\ldots & 22 & 1, 0, 6, 18, 114, 660, 3930, 25620,\ldots & 64 & 1, 0, 12, 0, 540, 0, 33600, 0,\ldots & 106 & 1, 0, 36, 348, 6516, 110880, 2069820,\ldots & 148 \\
1, 0, 4, 0, 36, 60, 400, 1680, 4900,\ldots & 23 & 1, 0, 6, 18, 114, 720, 4290, 28980,\ldots & 65 & 1, 0, 12, 30, 396, 2160, 20370,\ldots & 107 & 1, 0, 44, 528, 11292, 228000,\ldots & 149 \\
1, 0, 4, 0, 60, 0, 1120, 0, 24220, 0,\ldots & 24 & 1, 0, 6, 18, 138, 720, 5010, 32340,\ldots & 66 & 1, 0, 12, 36, 420, 2700, 24420,\ldots & 108 & 1, 0, 48, 600, 13176, 276480,\ldots & 150 \\
1, 0, 4, 0, 60, 60, 1120, 1680,\ldots & 25 & 1, 0, 6, 18, 138, 780, 5370, 36120,\ldots & 67 & 1, 0, 12, 36, 564, 3600, 41700,\ldots & 109 & 1, 0, 54, 492, 10122, 164160,\ldots & 151 \\
1, 0, 4, 6, 36, 120, 490, 2520, 8260,\ldots & 26 & 1, 0, 6, 24, 138, 960, 6180, 43680,\ldots & 68 & 1, 0, 12, 42, 468, 3360, 31350,\ldots & 110 & 1, 0, 54, 510, 10170, 168840,\ldots & 152 \\
1, 0, 4, 6, 36, 180, 490, 3780,\ldots & 27 & 1, 0, 6, 24, 138, 1080, 6540, 50400,\ldots & 69 & 1, 0, 12, 48, 540, 4320, 42240,\ldots & 111 & 1, 0, 54, 528, 10698, 184320,\ldots & 153 \\
1, 0, 4, 6, 36, 180, 490, 4200,\ldots & 28 & 1, 0, 6, 24, 162, 1080, 7620, 55440,\ldots & 70 & 1, 0, 12, 54, 540, 4620, 43770,\ldots & 112 & 1, 0, 54, 672, 15642, 336960,\ldots & 154 \\
1, 0, 4, 6, 60, 120, 1210, 3360,\ldots & 29 & 1, 0, 6, 30, 138, 1260, 7710, 57960,\ldots & 71 & 1, 0, 12, 60, 636, 5760, 58620,\ldots & 113 & 1, 0, 56, 492, 10536, 168600,\ldots & 155 \\
1, 0, 4, 6, 60, 180, 1210, 5040,\ldots & 30 & 1, 0, 6, 30, 186, 1380, 10230, 78540,\ldots & 72 & 1, 0, 14, 48, 594, 4200, 41900,\ldots & 114 & 1, 0, 56, 528, 11112, 189180,\ldots & 156 \\
1, 0, 4, 6, 60, 180, 1210, 5460,\ldots & 31 & 1, 0, 6, 30, 210, 1440, 11310, 87780,\ldots & 73 & 1, 0, 14, 48, 642, 4680, 49820,\ldots & 115 & 1, 0, 58, 600, 13182, 247440,\ldots & 157 \\
1, 0, 4, 12, 36, 240, 940, 4200,\ldots & 32 & 1, 0, 6, 48, 282, 2400, 22020,\ldots & 74 & 1, 0, 14, 60, 666, 5640, 56120,\ldots & 116 & 1, 0, 66, 816, 20214, 449640,\ldots & 158 \\
1, 0, 4, 12, 36, 240, 940, 4620,\ldots & 33 & 1, 0, 8, 0, 216, 0, 8000, 0, 343000,\ldots & 75 & 1, 0, 14, 66, 762, 6960, 73490,\ldots & 117 & 1, 0, 68, 960, 28116, 689040,\ldots & 159 \\
1, 0, 4, 12, 36, 300, 940, 6300,\ldots & 34 & 1, 0, 8, 12, 168, 600, 5300, 27720,\ldots & 76 & 1, 0, 14, 72, 882, 8400, 95180,\ldots & 118 & 1, 0, 78, 1320, 37746, 1051920,\ldots & 160 \\
1, 0, 4, 12, 36, 360, 940, 8400,\ldots & 35 & 1, 0, 8, 12, 192, 600, 6740, 30240,\ldots & 77 & 1, 0, 14, 84, 930, 9720, 108680,\ldots & 119 & 1, 0, 90, 1518, 46086, 1327320,\ldots & 161 \\
1, 0, 4, 12, 60, 240, 1660, 6720,\ldots & 36 & 1, 0, 8, 12, 216, 720, 8540, 42000,\ldots & 78 & 1, 0, 14, 108, 1074, 13440, 154760,\ldots & 120 & 1, 0, 104, 1752, 56424, 1677120,\ldots & 162 \\
1, 0, 4, 12, 60, 300, 1660, 8820,\ldots & 37 & 1, 0, 8, 18, 168, 840, 5750, 37380,\ldots & 79 & 1, 0, 16, 72, 912, 8280, 91600,\ldots & 121 & 1, 0, 152, 3840, 157656, 6428160,\ldots & 163 \\
1, 0, 4, 12, 60, 360, 1660, 10920,\ldots & 38 & 1, 0, 8, 18, 168, 900, 6110, 42000,\ldots & 80 & 1, 0, 16, 90, 1104, 11460, 133990,\ldots & 122 & 1, 0, 396, 17616, 1217052, 85220640,\ldots & 164 \\
1, 0, 4, 12, 84, 360, 2380, 13440,\ldots & 39 & 1, 0, 8, 18, 192, 960, 7550, 49980,\ldots & 81 & 1, 0, 18, 84, 1446, 12960, 186840,\ldots & 123 & 1, 0, 1944, 215808, 35295192,\ldots & 165 \\
1, 0, 4, 12, 84, 420, 2380, 15120,\ldots & 40 & 1, 0, 8, 24, 192, 1200, 8360, 60900,\ldots & 82 & 1, 0, 18, 120, 1566, 18360, 237060,\ldots & 124 & \\
1, 0, 4, 18, 60, 480, 2470, 14280,\ldots & 41 & 1, 0, 8, 24, 216, 1320, 10160, 74760,\ldots & 83 & 1, 0, 20, 96, 1188, 10860, 114320,\ldots & 125 & \\
1, 0, 4, 18, 84, 540, 3190, 20160,\ldots & 42 & 1, 0, 8, 24, 240, 1440, 11960, 89040,\ldots & 84 & 1, 0, 20, 96, 1236, 10800, 119360,\ldots & 126 & \\
\bottomrule \\
\end{tabular}
\end{table}

\newpage
%\pagebreak

\pdfbookmark[1]{Appendix B: Mutations Between Minkowski Polynomials}{AppendixB}
\begin{center}
  {\Large \bf Appendix B: Mutations Between Minkowski Polynomials}
\end{center}
\section*{How To Read These Tables}

A typical table row is shown in Figure~\ref{fig:tablerow} below.  The
entry $f$ is a Laurent polynomial in variables $x$, $y$, and $z$.  Its
Newton polytope $\mathrm{Newt}(f)$ is the three-dimensional reflexive
polytope with ID equal to $k$ in the Graded Ring Database.  The
expressions $\alpha_1$, $\beta_1$, and $\gamma_1$ are rational
functions in $x$, $y$, and $z$, and there is a mutation $\phi \colon (x, y,
z) \mapsto (\alpha_1,\beta_1,\gamma_1)$ which relates $f$ to the
Laurent polynomial $g_1$ with ID $l_1$ in the same table.  Thus evaluating
$f(\alpha_1,\beta_1,\gamma_1)$ yields $g_1$.  Similarly, there is a mutation
$\psi:(x, y, z) \mapsto (\alpha_2,\beta_2,\gamma_2)$ which relates $f$
to the Laurent polynomial $g_2$ with ID $l_2$ in the same table: evaluating
$f(\alpha_2,\beta_2,\gamma_2)$ yields $g_2$.

\addtocounter{figure}{-1}

\begin{figure}[!h]
\centering
\footnotesize
\begin{tabular}{cp{0ex}cp{0ex}cl}

\toprule \multicolumn{1}{c}{{Node}}&& \multicolumn{1}{c}{{Laurent polynomial}} && \multicolumn{2}{c}{{Mutations}} \\ \midrule

$\vdots$ && $\vdots$ &&  & $\vdots$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
$k$ && $f$ && $l_1 \colon {}$ & $\left(\alpha_1,\beta_1,\gamma_1\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $l_2 \colon {}$ & $\left(\alpha_2,\beta_2,\gamma_2\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $\vdots$ & $\vdots$
 \bottomspacer \\ \addlinespace[1.1ex]
$\vdots$ && $\vdots$ &&  & $\vdots$ \bottomspacer \\ \bottomrule
\end{tabular}
\caption{A typical table row}
\label{fig:tablerow}
\end{figure}

\section*{Bucket 1}

\input{appendix_files/1}

\section*{Bucket 2}

\input{appendix_files/2}

\pagebreak

\section*{Bucket 3}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/3-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:3a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/3-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:3b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 3}
\end{figure}

\begin{textblock}{0.1}(0.76,0.12) \input{appendix_files/3-legend} \end{textblock}

\input{appendix_files/3-table}

\pagebreak

\section*{Bucket 4}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/4-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:4a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1cm}
    \includegraphics[width=5cm]{appendix_files/4-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:4b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 4}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/4-legend} \end{textblock}

\input{appendix_files/4-table}

\pagebreak

\section*{Bucket 5}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/5-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:5a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1cm}
    \includegraphics[width=5cm]{appendix_files/5-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:5b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 5}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/5-legend} \end{textblock}

\input{appendix_files/5-table}

\pagebreak

\section*{Bucket 6}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 6 consists of a single Laurent polynomial:
\[
f = \frac{x^2}{yz}+x+y+z+\frac{1}{x}
\]
The Newton polytope of $f$ has reflexive ID 8.
\section*{Bucket 7}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/7-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:7a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/7-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:7b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 7}
\end{figure}

\input{appendix_files/7-table}

\pagebreak

\section*{Bucket 8}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/8-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:8a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/8-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:8b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 8}
\end{figure}

\input{appendix_files/8-table}

\pagebreak

\section*{Bucket 9}

\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/9-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:9a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/9-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:9b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 9}
\end{figure}

\input{appendix_files/9-table}

\pagebreak

\section*{Bucket 10}

\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/10-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:10a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/10-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:10b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 10}
\end{figure}

\input{appendix_files/10-table}

\pagebreak

\section*{Bucket 11}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/11-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:11a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/11-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:11b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 11}
\end{figure}

\input{appendix_files/11-table}

\pagebreak

\section*{Bucket 12}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/12-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:12a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/12-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:12b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 12}
\end{figure}

\input{appendix_files/12-table}

\pagebreak

\section*{Bucket 13}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/13-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:13a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1cm}
    \includegraphics[width=6cm]{appendix_files/13-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:13b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 13}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/13-legend} \end{textblock}

\input{appendix_files/13-table}

\pagebreak

\section*{Bucket 14}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/14-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:14a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/14-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:14b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 14}
\end{figure}

\input{appendix_files/14-table}

\pagebreak

\section*{Bucket 15}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/15-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:15a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{0.8cm}
    \includegraphics[width=7cm]{appendix_files/15-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:15b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 15}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/15-legend} \end{textblock}

\input{appendix_files/15-table}

\pagebreak

\section*{Bucket 16}

\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/16-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:16a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/16-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:16b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 16}
\end{figure}

\input{appendix_files/16-table}

\pagebreak

\section*{Bucket 17}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/17-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:17a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/17-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:17b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 17}
\end{figure}

\begin{textblock}{0.1}(0.76,0.12) \input{appendix_files/17-legend} \end{textblock}

\input{appendix_files/17-table}

\pagebreak

\section*{Bucket 18}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/18-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 18}
  \label{fig:18a}
\end{figure}

\pagebreak

\input{appendix_files/18-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/18-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 18}
  \label{fig:18b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/18-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 19}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/19-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 19}
  \label{fig:19a}
\end{figure}

\pagebreak

\input{appendix_files/19-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/19-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 19}
  \label{fig:19b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/19-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 20}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/20-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:20a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/20-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:20b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 20}
\end{figure}

\begin{textblock}{0.1}(0.76,0.15) \input{appendix_files/20-legend} \end{textblock}

\pagebreak

\input{appendix_files/20-table}

\pagebreak

\section*{Bucket 21}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/21-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 21}
  \label{fig:21a}
\end{figure}

\pagebreak

\input{appendix_files/21-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/21-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 21}
  \label{fig:21b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/21-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 22}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/22-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:22a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/22-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:22b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 22}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/22-legend} \end{textblock}

\pagebreak

\input{appendix_files/22-table}

\pagebreak

\section*{Bucket 23}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 23 consists of a single Laurent polynomial:
\[
f = x+y+\frac{y}{z}+z+\frac{2}{x}+\frac{1}{x^2y}
\]
The Newton polytope of $f$ has reflexive ID 15.


\section*{Bucket 24}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/24-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:24a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1.2cm}
    \includegraphics[width=8cm]{appendix_files/24-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:24b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 24}
\end{figure}

\begin{textblock}{0.1}(0.76,0.32) \input{appendix_files/24-legend} \end{textblock}

\pagebreak

\input{appendix_files/24-table}

\pagebreak

\section*{Bucket 25}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/25-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:25a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/25-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:25b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 25}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/25-legend} \end{textblock}

\input{appendix_files/25-table}

\pagebreak

\section*{Bucket 26}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/26-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:26a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/26-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:26b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 26}
\end{figure}

\input{appendix_files/26-table}

\section*{Bucket 27}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 27 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{y}{x}+\frac{y}{xz}+\frac{2}{x}+\frac{1}{xy}
\]
The Newton polytope of $f$ has reflexive ID 58.

\pagebreak

\section*{Bucket 28}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6.8cm]{appendix_files/28-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:28a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6.8cm]{appendix_files/28-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:28b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 28}
\end{figure}


\input{appendix_files/28-table}

\section*{Bucket 29}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/29-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:29a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/29-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:29b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 29}
\end{figure}

\input{appendix_files/29-table}

\pagebreak

\section*{Bucket 30}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/30-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:30a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/30-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:30b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 30}
\end{figure}

\input{appendix_files/30-table}

\pagebreak

\section*{Bucket 31}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/31-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 31}
  \label{fig:31a}
\end{figure}

\pagebreak

\input{appendix_files/31-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/31-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 31}
  \label{fig:31b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/31-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 32}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/32-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:32a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/32-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:32b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 32}
\end{figure}

\input{appendix_files/32-table}

\pagebreak

\section*{Bucket 33}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3cm]{appendix_files/33-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:33a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3cm]{appendix_files/33-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:33b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 33}
\end{figure}

\input{appendix_files/33-table}

\pagebreak

\section*{Bucket 34}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/34-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:34a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/34-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:34b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 34}
\end{figure}



\pagebreak

\input{appendix_files/34-table}

\pagebreak

\section*{Bucket 35}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/35-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 35}
  \label{fig:35a}
\end{figure}

\pagebreak

\input{appendix_files/35-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/35-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 35}
  \label{fig:35b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.12) \input{appendix_files/35-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 36}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/36-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:36a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1.8cm}
    \includegraphics[width=8cm]{appendix_files/36-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:36b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 36}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/36-legend} \end{textblock}

\pagebreak

\input{appendix_files/36-table}

\pagebreak

\section*{Bucket 37}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/37-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 37}
  \label{fig:37a}
\end{figure}

\pagebreak

\input{appendix_files/37-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/37-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 37}
  \label{fig:37b}
\end{figure}

\begin{textblock}{0.1}(0.75,0.13) \input{appendix_files/37-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 38}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/38-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 38}
  \label{fig:38a}
\end{figure}

\pagebreak

\input{appendix_files/38-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/38-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 38}
  \label{fig:38b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.14) \input{appendix_files/38-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 39}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/39-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 39}
  \label{fig:39a}
\end{figure}

\pagebreak

\input{appendix_files/39-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/39-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 39}
  \label{fig:39b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.135) \input{appendix_files/39-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 40}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=10cm]{appendix_files/40-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:40a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1.6cm}
    \includegraphics[width=10cm]{appendix_files/40-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:40b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 40}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/40-legend} \end{textblock}

\pagebreak

\input{appendix_files/40-table}

\pagebreak

\section*{Bucket 41}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/41-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 41}
  \label{fig:41a}
\end{figure}

\pagebreak

\input{appendix_files/41-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/41-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 41}
  \label{fig:41b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.14) \input{appendix_files/41-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 42}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/42-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 42}
  \label{fig:42a}
\end{figure}

\pagebreak

\input{appendix_files/42-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/42-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 42}
  \label{fig:42b}
\end{figure}

\begin{textblock}{0.1}(0.73,0.13) \input{appendix_files/42-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 43}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/43-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 43}
  \label{fig:43a}
\end{figure}

\pagebreak

\input{appendix_files/43-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/43-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 43}
  \label{fig:43b}
\end{figure}

\begin{textblock}{0.1}(0.11,0.14) \input{appendix_files/43-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 44}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/44-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 44}
  \label{fig:44a}
\end{figure}

\pagebreak

\input{appendix_files/44-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/44-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 44}
  \label{fig:44b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.14) \input{appendix_files/44-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 45}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/45-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:45a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/45-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:45b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 45}
\end{figure}

\input{appendix_files/45-table}

\pagebreak

\section*{Bucket 46}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5.7cm]{appendix_files/46-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:46a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{-0.2cm}
    \includegraphics[width=5.7cm]{appendix_files/46-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:46b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 46}
\end{figure}

\begin{textblock}{0.1}(0.76,0.13) \input{appendix_files/46-legend} \end{textblock}

\input{appendix_files/46-table}

\section*{Bucket 47}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3cm]{appendix_files/47-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:47a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3cm]{appendix_files/47-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:47b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 47}
\end{figure}

\input{appendix_files/47-table}


\section*{Bucket 48}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/48-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 48}
  \label{fig:48a}
\end{figure}

\pagebreak

\input{appendix_files/48-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/48-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 48 are of width 2}
  \label{fig:48b}
\end{figure}



\subfiguresend

\pagebreak

\section*{Bucket 49}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/49-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 49}
  \label{fig:49a}
\end{figure}

\pagebreak

\input{appendix_files/49-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/49-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 49}
  \label{fig:49b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/49-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 50}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 50 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{3}{x}+\frac{2}{xy}+\frac{3}{x^2y}+\frac{1}{x^3y^2}+\frac{1}{x^3y^2z}
\]
The Newton polytope of $f$ has reflexive ID 110.
\section*{Bucket 51}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 51 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{3}{x}+\frac{2}{xy}+\frac{3}{x^2y}+\frac{1}{x^2yz}+\frac{1}{x^3y^2}
\]
The Newton polytope of $f$ has reflexive ID 111.
\section*{Bucket 52}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/52-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:52a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/52-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:52b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 52}
\end{figure}

\input{appendix_files/52-table}

\pagebreak

\section*{Bucket 53}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=10cm]{appendix_files/53-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:53a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=10cm]{appendix_files/53-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:53b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 53}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/53-legend} \end{textblock}

\pagebreak

\input{appendix_files/53-table}

\pagebreak

\section*{Bucket 54}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/54-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 54}
  \label{fig:54a}
\end{figure}

\pagebreak

\input{appendix_files/54-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/54-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 54}
  \label{fig:54b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.13) \input{appendix_files/54-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 55}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5.5cm]{appendix_files/55-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:55a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5.5cm]{appendix_files/55-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:55b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 55}
\end{figure}


\input{appendix_files/55-table}

\pagebreak

\section*{Bucket 56}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/56-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:56a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/56-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:56b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 56}
\end{figure}

\input{appendix_files/56-table}

\pagebreak

\section*{Bucket 57}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/57-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 57}
  \label{fig:57a}
\end{figure}

\pagebreak

\input{appendix_files/57-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/57-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 57}
  \label{fig:57b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/57-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 58}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/58-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 58}
  \label{fig:58a}
\end{figure}

\pagebreak

\input{appendix_files/58-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/58-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 58}
  \label{fig:58b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/58-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 59}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/59-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 59}
  \label{fig:59a}
\end{figure}

\pagebreak

\input{appendix_files/59-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/59-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 59}
  \label{fig:59b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/59-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 60}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 60 consists of a single Laurent polynomial:
\[
f = x+y+\frac{y}{z}+z+\frac{3}{x}+\frac{2}{xy}+\frac{3}{x^2y}+\frac{1}{x^3y^2}
\]
The Newton polytope of $f$ has reflexive ID 116.

\section*{Bucket 61}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 61 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{3}{x}+\frac{1}{xz}+\frac{2}{xy}+\frac{3}{x^2y}+\frac{1}{x^3y^2}
\]
The Newton polytope of $f$ has reflexive ID 113.

\section*{Bucket 62}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/62-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:62a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/62-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:62b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 62}
\end{figure}



\pagebreak

\input{appendix_files/62-table}

\pagebreak

\section*{Bucket 63}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/63-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:63a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=6cm]{appendix_files/63-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:63b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 63}
\end{figure}

\begin{textblock}{0.1}(0.76,0.15) \input{appendix_files/63-legend} \end{textblock}

\input{appendix_files/63-table}

\pagebreak

\section*{Bucket 64}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm]{appendix_files/64-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 64}
  \label{fig:64a}
\end{figure}

\pagebreak

\input{appendix_files/64-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/64-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 64 are of width 2}
  \label{fig:64b}
\end{figure}



\subfiguresend

\pagebreak

\section*{Bucket 65}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/65-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 65}
  \label{fig:65a}
\end{figure}

\pagebreak

\input{appendix_files/65-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/65-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 65}
  \label{fig:65b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/65-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 66}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/66-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 66}
  \label{fig:66a}
\end{figure}

\pagebreak

\input{appendix_files/66-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/66-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 66}
  \label{fig:66b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/66-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 67}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/67-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 67}
  \label{fig:67a}
\end{figure}

\pagebreak

\input{appendix_files/67-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/67-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 67}
  \label{fig:67b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/67-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 68}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/68-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 68}
  \label{fig:68a}
\end{figure}

\pagebreak

\input{appendix_files/68-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/68-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 68}
  \label{fig:68b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/68-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 69}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/69-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 69}
  \label{fig:69a}
\end{figure}

\pagebreak

\input{appendix_files/69-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/69-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 69}
  \label{fig:69b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/69-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 70}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/70-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 70}
  \label{fig:70a}
\end{figure}

\pagebreak

\input{appendix_files/70-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/70-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 70}
  \label{fig:70b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/70-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 71}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/71-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 71}
  \label{fig:71a}
\end{figure}

\pagebreak

\input{appendix_files/71-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/71-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 71}
  \label{fig:71b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/71-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 72}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/72-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 72}
  \label{fig:72a}
\end{figure}

\pagebreak

\input{appendix_files/72-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/72-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 72}
  \label{fig:72b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/72-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 73}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/73-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 73}
  \label{fig:73a}
\end{figure}

\pagebreak

\input{appendix_files/73-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/73-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 73}
  \label{fig:73b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/73-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 74}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/74-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 74}
  \label{fig:74a}
\end{figure}

\input{appendix_files/74-table}

\pagebreak


\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/74-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 74}
  \label{fig:74b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/74-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 75}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/75-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:75a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/75-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:75b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 75}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/75-legend} \end{textblock}

\pagebreak

\input{appendix_files/75-table}

\pagebreak

\section*{Bucket 76}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/76-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 76}
  \label{fig:76a}
\end{figure}

\pagebreak

\input{appendix_files/76-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/76-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 76 are of width 2}
  \label{fig:76b}
\end{figure}



\subfiguresend

\pagebreak

\section*{Bucket 77}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/77-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 77}
  \label{fig:77a}
\end{figure}

\pagebreak

\input{appendix_files/77-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/77-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 77}
  \label{fig:77b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/77-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 78}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/78-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 78}
  \label{fig:78a}
\end{figure}

\pagebreak

\input{appendix_files/78-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/78-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 78}
  \label{fig:78b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/78-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 79}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/79-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:79a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/79-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:79b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 79}
\end{figure}



\pagebreak

\input{appendix_files/79-table}

\pagebreak

\section*{Bucket 80}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/80-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 80}
  \label{fig:80a}
\end{figure}

\pagebreak

\input{appendix_files/80-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/80-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 80}
  \label{fig:80b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/80-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 81}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/81-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 81}
  \label{fig:81a}
\end{figure}

\pagebreak

\input{appendix_files/81-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/81-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 81}
  \label{fig:81b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/81-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 82}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/82-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 82}
  \label{fig:82a}
\end{figure}

\pagebreak

\input{appendix_files/82-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/82-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 82}
  \label{fig:82b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/82-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 83}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/83-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 83}
  \label{fig:83a}
\end{figure}

\pagebreak

\input{appendix_files/83-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/83-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 83}
  \label{fig:83b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/83-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 84}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/84-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 84}
  \label{fig:84a}
\end{figure}

\pagebreak

\input{appendix_files/84-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/84-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 84}
  \label{fig:84b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/84-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 85}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/85-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 85}
  \label{fig:85a}
\end{figure}

\pagebreak

\input{appendix_files/85-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/85-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 85}
  \label{fig:85b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/85-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 86}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/86-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 86}
  \label{fig:86a}
\end{figure}

\pagebreak

\input{appendix_files/86-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/86-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 86}
  \label{fig:86b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/86-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 87}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/87-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 87}
  \label{fig:87a}
\end{figure}

\pagebreak

\input{appendix_files/87-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/87-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 87}
  \label{fig:87b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/87-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 88}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/88-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 88}
  \label{fig:88a}
\end{figure}

\pagebreak

\input{appendix_files/88-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/88-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 88}
  \label{fig:88b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.13) \input{appendix_files/88-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 89}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/89-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 89}
  \label{fig:89a}
\end{figure}

\pagebreak

\input{appendix_files/89-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/89-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 89}
  \label{fig:89b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/89-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 90}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 90 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{2}{y}+\frac{y}{x}+\frac{3}{x}+\frac{3}{xy}+\frac{1}{xy^2}+\frac{1}{xy^2z}
\]
The Newton polytope of $f$ has reflexive ID 279.

\section*{Bucket 91}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 91 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{2}{y}+\frac{y^2}{xz}+\frac{y}{x}+\frac{3}{x}+\frac{3}{xy}+\frac{1}{xy^2}
\]
The Newton polytope of $f$ has reflexive ID 268.
\section*{Bucket 92}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 92 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{2}{y}+\frac{y}{x}+\frac{3}{x}+\frac{3}{xy}+\frac{1}{xyz}+\frac{1}{xy^2}
\]
The Newton polytope of $f$ has reflexive ID 280.

\pagebreak

\section*{Bucket 93}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/93-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:93a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/93-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:93b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 93}
\end{figure}

\input{appendix_files/93-table}


\section*{Bucket 94}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 94 consists of a single Laurent polynomial:
\[
f = x+\frac{x}{y}+\frac{x}{yz}+y+z+\frac{3}{y}+\frac{2}{x}+\frac{3}{xy}+\frac{1}{x^2y}
\]
The Newton polytope of $f$ has reflexive ID 288.

\pagebreak

\section*{Bucket 95}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/95-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 95}
  \label{fig:95a}
\end{figure}

\pagebreak

\input{appendix_files/95-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/95-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 95}
  \label{fig:95b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.14) \input{appendix_files/95-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 96}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 96 consists of a single Laurent polynomial:
\[
f = x+y+z+\frac{2}{y}+\frac{y}{x}+\frac{3}{x}+\frac{1}{xz}+\frac{3}{xy}+\frac{1}{xy^2}
\]
The Newton polytope of $f$ has reflexive ID 281.

\section*{Bucket 97}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/97-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:97a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/97-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:97b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 97}
\end{figure}

\pagebreak

\input{appendix_files/97-table}

\pagebreak

\section*{Bucket 98}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/98-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:98a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/98-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:98b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 98}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/98-legend} \end{textblock}

\pagebreak

\input{appendix_files/98-table}

\pagebreak

\section*{Bucket 99}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/99-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 99}
  \label{fig:99a}
\end{figure}

\pagebreak

\input{appendix_files/99-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/99-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 99}
  \label{fig:99b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.13) \input{appendix_files/99-legend} \end{textblock}

\subfiguresend


\pagebreak

\section*{Bucket 100}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/100-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 100}
  \label{fig:100a}
\end{figure}

\pagebreak

\input{appendix_files/100-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/100-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 100}
  \label{fig:100b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.15) \input{appendix_files/100-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 101}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/101-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 101}
  \label{fig:101a}
\end{figure}

\pagebreak

\input{appendix_files/101-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/101-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 101}
  \label{fig:101b}
\end{figure}

\begin{textblock}{0.1}(0.07,0.12) \input{appendix_files/101-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 102}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/102-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 102}
  \label{fig:102a}
\end{figure}

\pagebreak

\input{appendix_files/102-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/102-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 102}
  \label{fig:102b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/102-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 103}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/103-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 103}
  \label{fig:103a}
\end{figure}

\pagebreak

\input{appendix_files/103-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/103-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 103}
  \label{fig:103b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/103-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 104}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/104-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 104}
  \label{fig:104a}
\end{figure}

\pagebreak

\input{appendix_files/104-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/104-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 104}
  \label{fig:104b}
\end{figure}

\begin{textblock}{0.1}(0.09,0.12) \input{appendix_files/104-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 105}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/105-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 105}
  \label{fig:105a}
\end{figure}

\pagebreak

\input{appendix_files/105-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/105-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 105}
  \label{fig:105b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/105-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 106}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/106-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:106a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/106-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:106b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 106}
\end{figure}

\input{appendix_files/106-table}

\pagebreak

\section*{Bucket 107}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/107-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:107a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/107-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:107b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 107}
\end{figure}


\input{appendix_files/107-table}

\pagebreak

\section*{Bucket 108}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/108-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 108}
  \label{fig:108a}
\end{figure}

\pagebreak

\input{appendix_files/108-table}

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/108-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 108}
  \label{fig:108b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/108-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 109}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/109-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 109}
  \label{fig:109a}
\end{figure}

\pagebreak

\input{appendix_files/109-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/109-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 109}
  \label{fig:109b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/109-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 110}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/110-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 110}
  \label{fig:110a}
\end{figure}

\pagebreak

\input{appendix_files/110-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/110-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 110}
  \label{fig:110b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/110-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 111}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/111-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 111}
  \label{fig:111a}
\end{figure}

\pagebreak

\input{appendix_files/111-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/111-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 111}
  \label{fig:111b}
\end{figure}

\begin{textblock}{0.1}(0.09,0.13) \input{appendix_files/111-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 112}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/112-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 112}
  \label{fig:112a}
\end{figure}

\pagebreak

\input{appendix_files/112-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/112-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 112}
  \label{fig:112b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/112-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 113}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/113-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 113}
  \label{fig:113a}
\end{figure}

\pagebreak

\input{appendix_files/113-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/113-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 113}
  \label{fig:113b}
\end{figure}

\begin{textblock}{0.1}(0.07,0.09) \input{appendix_files/113-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 114}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=10cm]{appendix_files/114-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:114a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=10cm]{appendix_files/114-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:114b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 114}
\end{figure}



\pagebreak

\input{appendix_files/114-table}

\pagebreak

\section*{Bucket 115}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/115-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 115}
  \label{fig:115a}
\end{figure}

\pagebreak

\input{appendix_files/115-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/115-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 115}
  \label{fig:115b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/115-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 116}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/116-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 116}
  \label{fig:116a}
\end{figure}

\pagebreak

\input{appendix_files/116-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/116-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 116}
  \label{fig:116b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/116-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 117}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/117-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 117}
  \label{fig:117a}
\end{figure}

\pagebreak

\input{appendix_files/117-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/117-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 117}
  \label{fig:117b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/117-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 118}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/118-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 118}
  \label{fig:118a}
\end{figure}

\pagebreak

\input{appendix_files/118-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/118-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 118}
  \label{fig:118b}
\end{figure}

\begin{textblock}{0.1}(0.72,0.15) \input{appendix_files/118-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 119}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/119-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 119}
  \label{fig:119a}
\end{figure}

\pagebreak

\input{appendix_files/119-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/119-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 119}
  \label{fig:119b}
\end{figure}

\begin{textblock}{0.1}(0.07,0.09) \input{appendix_files/119-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 120}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/120-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 120}
  \label{fig:120a}
\end{figure}

\pagebreak

\input{appendix_files/120-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/120-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 120}
  \label{fig:120b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/120-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 121}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/121-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 121}
  \label{fig:121a}
\end{figure}

\pagebreak

\input{appendix_files/121-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/121-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 121}
  \label{fig:121b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/121-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 122}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/122-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 122}
  \label{fig:122a}
\end{figure}

\pagebreak

\input{appendix_files/122-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/122-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 122}
  \label{fig:122b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/122-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 123}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/123-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:123a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{0.2cm}
    \includegraphics[width=8cm]{appendix_files/123-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:123b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 123}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/123-legend} \end{textblock}

\pagebreak

\input{appendix_files/123-table}

\pagebreak

\section*{Bucket 124}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=15cm]{appendix_files/124-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 124}
  \label{fig:124a}
\end{figure}

\pagebreak

\input{appendix_files/124-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \vspace{2cm}
  \includegraphics[width=15cm]{appendix_files/124-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 124}
  \label{fig:124b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.13) \input{appendix_files/124-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 125}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 125 consists of a single Laurent polynomial:
\[
f = xy^2+\frac{xy^2}{z}+2xy+x+4y+z+\frac{6}{x}+\frac{2}{xy}+\frac{4}{x^2y}+\frac{1}{x^3y^2}
\]
The Newton polytope of $f$ has reflexive ID 457.
\section*{Bucket 126}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 126 consists of a single Laurent polynomial:
\[
f = xy^2z^2+2xyz+x+4yz+y+z+\frac{6}{x}+\frac{2}{xyz}+\frac{4}{x^2yz}+\frac{1}{x^3y^2z^2}
\]
The Newton polytope of $f$ has reflexive ID 453.
\section*{Bucket 127}

\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/127-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:127a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/127-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:127b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 127}
\end{figure}


\input{appendix_files/127-table}

\pagebreak

\section*{Bucket 128}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/128-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 128}
  \label{fig:128a}
\end{figure}

\pagebreak

\input{appendix_files/128-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/128-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 128}
  \label{fig:128b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/128-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 129}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 129 consists of a single Laurent polynomial:
\[
f = xz^2+2xz+x+y+4z+\frac{6}{x}+\frac{2}{xz}+\frac{1}{xy}+\frac{4}{x^2z}+\frac{1}{x^3z^2}
\]
The Newton polytope of $f$ has reflexive ID 452.

\section*{Bucket 130}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/130-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:130a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=4cm]{appendix_files/130-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:130b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 130}
\end{figure}

\input{appendix_files/130-table}

\pagebreak

\section*{Bucket 131}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/131-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:131a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{1cm}
    \includegraphics[width=5cm]{appendix_files/131-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:131b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 131}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/131-legend} \end{textblock}

\input{appendix_files/131-table}

\pagebreak

\section*{Bucket 132}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/132-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 132}
  \label{fig:132a}
\end{figure}

\pagebreak

\input{appendix_files/132-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=14cm,height=14cm,keepaspectratio]{appendix_files/132-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 132}
  \label{fig:132b}
\end{figure}

\begin{textblock}{0.1}(0.71,0.09) \input{appendix_files/132-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 133}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/133-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 133}
  \label{fig:133a}
\end{figure}

\pagebreak

\input{appendix_files/133-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/133-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 133}
  \label{fig:133b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.15) \input{appendix_files/133-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 134}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/134-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 134}
  \label{fig:134a}
\end{figure}

\pagebreak

\input{appendix_files/134-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/134-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 134}
  \label{fig:134b}
\end{figure}

\begin{textblock}{0.1}(0.15,0.14) \input{appendix_files/134-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 135}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/135-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 135}
  \label{fig:135a}
\end{figure}

\pagebreak

\input{appendix_files/135-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/135-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 135}
  \label{fig:135b}
\end{figure}

\begin{textblock}{0.1}(0.75,0.09) \input{appendix_files/135-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 136}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=9cm]{appendix_files/136-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:136a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=9cm]{appendix_files/136-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:136b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 136}
\end{figure}

\pagebreak

\input{appendix_files/136-table}

\pagebreak

\section*{Bucket 137}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/137-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 137}
  \label{fig:137a}
\end{figure}

\pagebreak

\input{appendix_files/137-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/137-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 137}
  \label{fig:137b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/137-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 138}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/138-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 138}
  \label{fig:138a}
\end{figure}

\pagebreak

\input{appendix_files/138-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/138-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 138}
  \label{fig:138b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/138-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 139}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/139-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 139}
  \label{fig:139a}
\end{figure}

\pagebreak

\input{appendix_files/139-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/139-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 139}
  \label{fig:139b}
\end{figure}

\begin{textblock}{0.1}(0.71,0.12) \input{appendix_files/139-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 140}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 140 consists of a single Laurent polynomial:
\[
f = xy^2+2xyz+2xy+xz^2+2xz+x+\frac{2}{xz}+\frac{2}{xy}+\frac{2}{xyz}+\frac{1}{x^3y^2z^2}
\]
The Newton polytope of $f$ has reflexive ID 428.

\section*{Bucket 141}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=11cm,keepaspectratio]{appendix_files/141-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 141}
  \label{fig:141a}
\end{figure}

\pagebreak

\input{appendix_files/141-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/141-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 141}
  \label{fig:141b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.15) \input{appendix_files/141-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 142}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/142-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 142}
  \label{fig:142a}
\end{figure}

\pagebreak

\input{appendix_files/142-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/142-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 142}
  \label{fig:142b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.15) \input{appendix_files/142-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 143}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/143-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 143}
  \label{fig:143a}
\end{figure}

\pagebreak

\input{appendix_files/143-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/143-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 143}
  \label{fig:143b}
\end{figure}

\begin{textblock}{0.1}(0.1,0.09) \input{appendix_files/143-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 144}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/144-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 144}
  \label{fig:144a}
\end{figure}

\pagebreak

\input{appendix_files/144-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/144-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 144}
  \label{fig:144b}
\end{figure}

\begin{textblock}{0.1}(0.72,0.12) \input{appendix_files/144-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 145}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/145-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 145}
  \label{fig:145a}
\end{figure}

\pagebreak

\input{appendix_files/145-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \vspace{1cm}
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/145-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 145}
  \label{fig:145b}
\end{figure}

\begin{textblock}{0.1}(0.09,0.15) \input{appendix_files/145-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 146}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/146-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:146a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=5cm]{appendix_files/146-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:146b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 146}
\end{figure}

\input{appendix_files/146-table}

\pagebreak

\section*{Bucket 147}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/147-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations between Minkowski polynomials in bucket 147}
  \label{fig:147a}
\end{figure}

\pagebreak

\input{appendix_files/147-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/147-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 147}
  \label{fig:147b}
\end{figure}

\begin{textblock}{0.1}(0.74,0.10) \input{appendix_files/147-legend} \end{textblock}

\subfiguresend

\pagebreak
\section*{Bucket 148}

Any two Minkowski polynomials in bucket 148 are connected by a
sequence of mutations, but it is not possible to insist that all of
the Laurent polynomials involved are Minkowski polynomials.  The
smallest number of additional Laurent polynomials that one needs to
add in order to connect up the bucket is two, and one can insist that
both of these Laurent polynomials $g$, $h$ have reflexive Newton
polytopes.  There are many possible choices for $g$ and $h$: one
such choice, together with a collection of mutations that together
connect any two Minkowski polynomials in bucket 148, is shown in
Figure~\ref{fig:148} and Table~\ref{table:148}.  The Laurent
polynomials $g$ and $h$ are indicated in red.


\begin{figure}[!h]
  \centering
  \includegraphics[width=12cm]{appendix_files/148-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations that connect up  Minkowski polynomials in bucket 148}
  \label{fig:148}
\end{figure}

\pagebreak

\input{appendix_files/148-table}

\pagebreak

\section*{Bucket 149}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/149-spanning-tree.pdf}
  \caption{Selected width-2 mutations between Minkowski polynomials in bucket 149}
  \label{fig:149a}
\end{figure}

\pagebreak

\input{appendix_files/149-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/149-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 149}
  \label{fig:149b}
\end{figure}

\begin{textblock}{0.1}(0.7,0.14) \input{appendix_files/149-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 150}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/150-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations between Minkowski polynomials in bucket 150}
  \label{fig:150a}
\end{figure}

\pagebreak

\input{appendix_files/150-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/150-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 150}
  \label{fig:150b}
\end{figure}

\begin{textblock}{0.1}(0.72,0.13) \input{appendix_files/150-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 151}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 151 consists of a single Laurent polynomial:
\[
f = xy^3+3xy^2+3xy+x+\frac{x}{z}+3y+z+\frac{3}{y}+\frac{3}{xy}+\frac{3}{xy^2}+\frac{1}{x^2y^3}
\]
The Newton polytope of $f$ has reflexive ID 771.
\section*{Bucket 152}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 152 consists of a single Laurent polynomial:
\[
f = x+\frac{3x}{yz}+\frac{3x}{y^2z^2}+\frac{x}{y^3z^3}+3yz+y+z+\frac{3}{yz}+\frac{3y^2z^2}{x}+\frac{3yz}{x}+\frac{y^3z^3}{x^2}
\]
The Newton polytope of $f$ has reflexive ID 770.
\section*{Bucket 153}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 153 consists of a single Laurent polynomial:
\[
f = xyz^2+xyz+xz^3+3xz^2+3xz+x+y+3z+\frac{3}{z}+\frac{1}{yz}+\frac{3}{xz}+\frac{3}{xz^2}+\frac{1}{x^2z^3}
\]
The Newton polytope of $f$ has reflexive ID 1651.

\pagebreak

\section*{Bucket 154}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/154-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations between Minkowski polynomials in bucket 154}
  \label{fig:154a}
\end{figure}

\pagebreak

\input{appendix_files/154-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \vspace{1cm}
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/154-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 154}
  \label{fig:154b}
\end{figure}

\begin{textblock}{0.1}(0.71,0.15) \input{appendix_files/154-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 155}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 155 consists of a single Laurent polynomial:
\[
f = x+yz^3+3yz^2+3yz+y+3z+\frac{3}{z}+\frac{3}{yz}+\frac{3}{yz^2}+\frac{1}{y^2z^3}+\frac{1}{x}
\]
The Newton polytope of $f$ has reflexive ID 769.
\section*{Bucket 156}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 156 consists of a single Laurent polynomial:
\[
f = xyz^2+xyz+3xz+x+\frac{3x}{y}+\frac{x}{y^2z}+3yz+y+\frac{3}{yz}+\frac{3y}{x}+\frac{1}{x}+\frac{3}{xz}+\frac{y}{x^2z}
\]
The Newton polytope of $f$ has reflexive ID 1605.
\section*{Bucket 157}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3.3cm]{appendix_files/157-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 mutations}
    \label{fig:157a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=3.3cm]{appendix_files/157-mutation-graph.pdf}
    \caption{All mutations are of width 2}
    \label{fig:157b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 157}
\end{figure}

\input{appendix_files/157-table}


\section*{Bucket 158}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/158-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 and width-3 mutations}
    \label{fig:158a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=7cm]{appendix_files/158-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:158b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 158}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/158-legend} \end{textblock}

\pagebreak

\input{appendix_files/158-table}

\section*{Bucket 159}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 159 consists of a single Laurent polynomial:
\[
\textstyle
f = xy^2+2xy+x+y^3z+3y^2z+3yz+2y+z+\frac{2}{y}+\frac{2}{yz}+\frac{2}{y^2z}+\frac{3}{x}+\frac{6}{xy}+\frac{3}{xy^2}+\frac{4}{xy^2z}+\frac{4}{xy^3z}+\frac{1}{xy^4z^2}+\frac{3}{x^2y^3z}+\frac{3}{x^2y^4z}+\frac{2}{x^2y^5z^2}+\frac{1}{x^3y^6z^2}
\]
The Newton polytope of $f$ has reflexive ID 3879.

\pagebreak

\section*{Bucket 160}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/160-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations between Minkowski polynomials in bucket 160}
  \label{fig:160a}
\end{figure}

\pagebreak

\input{appendix_files/160-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/160-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 160}
  \label{fig:160b}
\end{figure}

\begin{textblock}{0.1}(0.71,0.13) \input{appendix_files/160-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 161}

Any two Minkowski polynomials in bucket 161 are connected by a
sequence of mutations, but it is not possible to insist that all of
the Laurent polynomials involved are Minkowski polynomials.  The
smallest number of additional Laurent polynomials that one needs to
add in order to connect up the bucket is two, and one can insist that
both of these Laurent polynomials $g$, $h$ have reflexive Newton
polytopes.  There is a unique choice of such $g$ and $h$: this is
shown, together with a collection of mutations that together connect
any two Minkowski polynomials in bucket 161, in
Figure~\ref{fig:161} and Table~\ref{table:161}.  Note that the
collection of mutations connecting bucket 161 is not unique.  The
Laurent polynomials $g$ and $h$ are indicated in red.


\begin{figure}[!h]
  \centering
  \includegraphics[width=9cm,height=14cm,keepaspectratio]{appendix_files/161-spanning-tree.pdf}
  \caption{Selected width-2 mutations that connect up  Minkowski polynomials in bucket 161}
  \label{fig:161}
\end{figure}


\input{appendix_files/161-table}

\section*{Bucket 162}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 162 consists of a single Laurent polynomial:
\[
f = xy^2+2xy+x+\frac{2x}{z}+\frac{2x}{yz}+\frac{x}{y^2z^2}+y^3z+3y^2z+3yz+4y+z+\frac{4}{y}+\frac{5}{yz}+\frac{5}{y^2z}+\frac{2}{y^3z^2}+\frac{1}{x}+\frac{2}{xy}+\frac{1}{xy^2}+\frac{2}{xy^2z}+\frac{2}{xy^3z}+\frac{1}{xy^4z^2}
\]
The Newton polytope of $f$ has reflexive ID 3927.

\pagebreak

\section*{Bucket 163}


\subfiguresbegin

\begin{figure}[!h]
  \centering
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/163-spanning-tree.pdf}
  \caption{Selected width-2 and width-3 mutations between Minkowski polynomials in bucket 163}
  \label{fig:163a}
\end{figure}

\pagebreak

\input{appendix_files/163-table}

\pagebreak

\begin{figure}[!h]
  \centering
  \vspace{1cm}
  \includegraphics[width=17cm,height=14cm,keepaspectratio]{appendix_files/163-mutation-graph.pdf}
  \caption{All mutations between Minkowski polynomials in bucket 163}
  \label{fig:163b}
\end{figure}

\begin{textblock}{0.1}(0.71,0.12) \input{appendix_files/163-legend} \end{textblock}

\subfiguresend

\pagebreak

\section*{Bucket 164}


\begin{figure}[h!]
    \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \includegraphics[width=8cm]{appendix_files/164-spanning-tree.pdf}
    \caption{A spanning tree consisting of width-2 and width-3 mutations}
    \label{fig:164a}
  \end{subfigure}
  \qquad
  \begin{subfigure}[b]{0.4\textwidth}
    \centering
    \vspace{2.2cm}
    \includegraphics[width=8cm]{appendix_files/164-mutation-graph.pdf}
    \caption{All mutations}
    \label{fig:164b}
  \end{subfigure}
  \caption{Mutations between Minkowski polynomials in bucket 164}
\end{figure}

\begin{textblock}{0.1}(0.76,0.18) \input{appendix_files/164-legend} \end{textblock}

\pagebreak

\input{appendix_files/164-table}

\section*{Bucket 165}
\addtocounter{table}{1}
\addtocounter{figure}{1}

 Bucket 165 consists of a single Laurent polynomial:
 \begin{multline*}
   f =
   xy^4+4xy^3z+4xy^3+6xy^2z^2+12xy^2z+6xy^2+4xyz^3+12xyz^2+12xyz+4xy+xz^4+4xz^3+6xz^2+4xz+x+\frac{4y^2}{z}+12y+\frac{12y}{z}\\
   +12z+\frac{12}{z}
   +\frac{4z^2}{y}+\frac{12z}{y}+\frac{12}{y}+\frac{4}{yz}+\frac{6}{xz^2}+\frac{12}{xyz}+\frac{12}{xyz^2}+\frac{6}{xy^2}+\frac{12}{xy^2z}+\frac{6}{xy^2z^2}+\frac{4}{x^2y^2z^3}+\frac{4}{x^2y^3z^2}+\frac{4}{x^2y^3z^3}+\frac{1}{x^3y^4z^4}
 \end{multline*}
 The Newton polytope of $f$ has reflexive ID 4312.

\end{document} 