

\newcommand{\TableLabeledSimpleEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
	\begin{pgfonlayer}{edgelayer}
        \draw[style=plain edge] (0) edge["$m_{ij}$"] (1);
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableNoEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableSimpleEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
	\begin{pgfonlayer}{edgelayer}
        \draw[style=plain edge] (0) to (1);
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableDoubleEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
	\begin{pgfonlayer}{edgelayer}
        \draw[style=double edge] (0) to (1);
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableTripleEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
	\begin{pgfonlayer}{edgelayer}
        \draw[style=triple edge] (0) to (1);
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableBoldEdge}[0]{
\begin{tikzpicture}
    \begin{pgfonlayer}{nodelayer}
        \node [style=white node, label=$H_1$] (0) at (0, 0) {};
        \node [style=white node, label=$H_2$] (1) at (3, 0) {};
    \end{pgfonlayer}
    \begin{pgfonlayer}{edgelayer}
        \draw[style=thick edge] (0) to (1);
    \end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableDottedEdge}[0]{
\begin{tikzpicture}
	\begin{pgfonlayer}{nodelayer}
		\node [style=white node, label=$H_1$] (0) at (0, 0) {};
		\node [style=white node, label=$H_2$] (1) at (3, 0) {};
	\end{pgfonlayer}
	\begin{pgfonlayer}{edgelayer}
        \draw[style=dashed edge] (0) edge["$w_{ij}$"] (1);
	\end{pgfonlayer}
\end{tikzpicture}
}

\newcommand{\TableSimpleVertex}[0]{
\tikz[baseline]{\node [style=white node] (0) at (0, 0) {};}
}


\newcommand{\TableBlackVertex}[0]{
\tikz[baseline]{\node [style=black node] (0) at (0, 0) {};}
}

\newcommand{\TableDoubleVertex}[0]{
\tikz[baseline]{\node [style=doubled node] (0) at (0, 0) {};}
}

\begin{table}[H]
\centering
\resizebox{\textwidth}{!}{%
\begin{tabular}{@{}llllll@{}}
\toprule
Description           & Diagram            & Notation              & $m_{ij}$ & $\angle(H_i, H_j)$ & $w_{ij}$                 \\ \midrule
Labeled simple edge & \TableLabeledSimpleEdge & $H_i \transverse H_j$ & $m_{ij}$ & $\pi/m_{ij}$ & $\cos\qty{\pi \over m_{ij}}$ \\
No Edge               & \TableNoEdge       & $H_i \perp H_j$       & $2$      & $\pi/2$            & 0                        \\
Simple Edge           & \TableSimpleEdge   & $H_i \transverse H_j$ & $3$      & $\pi/3$            & $1\over 2$               \\
Double Edge           & \TableDoubleEdge   & $H_i \transverse H_j$ & $4$      & $\pi/4$            & $\sqrt{2} \over 2$       \\
Triple Edge           & \TableTripleEdge   & $H_i \transverse H_j$ & $5$      & $\pi/5$            & ${1 + \sqrt{5} \over 4}$ \\
Thick/bold edge       & \TableBoldEdge     & $H_i \parallel H_j$   & $\infty$ & $0$                & 1                        \\
Dotted Edge           & \TableDottedEdge   & $H_i \diverge H_j$    & $0$      & $\infty$           & $\cosh(\rho(H_i, H_j))$  \\\cmidrule{0-5}
Simple vertex         & \TableSimpleVertex & $h_i^2 = -1$          &          &                    & $1$                     \\
Black vertex          & \TableBlackVertex  & $h_i^2 = -2$          &          &                    & $2$                     \\
Double-circled vertex & \TableDoubleVertex & $h_i^2 = -4$          &          &                    & $4$                     \\ \bottomrule
\end{tabular}%
}
\caption{A summary of conventions for Coxeter-Vinberg diagrams}
\label{tab:coxeter-vinberg-conventions}
\end{table}