\begin{figure}[tp]
\centering
\begin{tikzpicture}[x=1cm, y=1cm, >={Stealth[length=1.6mm]}, font=\scriptsize]
\foreach \i/\L/\R/\B/\T/\nw/\ne/\sw/\se/\w/\dg in {
  0/1/1/1/1/1/0/0/-1/1/{\scriptsize NE$=$SW},
  1/-1/-1/-1/-1/-1/0/0/1/1/{\scriptsize NE$=$SW},
  2/1/1/-1/-1/1/2/0/1/1/{\scriptsize NW$=$SE},
  3/-1/-1/1/1/-1/-2/0/-1/1/{\scriptsize NW$=$SE},
  4/1/-1/-1/1/1/0/0/1/c/{\scriptsize both},
  5/-1/1/1/-1/-1/0/0/-1/c/{\scriptsize both}}{
  \pgfmathsetmacro{\x}{2.35*\i}
  \draw[->, line width=0.7pt] ({\x-0.44-0.36*\L},0) -- ({\x-0.44+0.36*\L},0);
  \draw[->, line width=0.7pt] ({\x+0.44-0.36*\R},0) -- ({\x+0.44+0.36*\R},0);
  \draw[->, line width=0.7pt] (\x,{-0.44-0.36*\B}) -- (\x,{-0.44+0.36*\B});
  \draw[->, line width=0.7pt] (\x,{0.44-0.36*\T}) -- (\x,{0.44+0.36*\T});
  \fill (\x,0) circle (1.1pt);
  \node at ({\x-0.42},0.42) {$\nw$};
  \node at ({\x+0.42},0.42) {$\ne$};
  \node at ({\x-0.42},-0.42) {$\sw$};
  \node at ({\x+0.42},-0.42) {$\se$};
  \node at (\x,-1.12) {weight $\w$};
  \node[black!65] at (\x,-1.45) {equal: \dg};
}
\end{tikzpicture}
\caption{The six vertex configurations with $a=b=1$, and the heights of the four surrounding faces,
normalised to $0$ on the lower left face (the face to the left of an arrow is one unit higher). A
vertex has weight $c$ exactly when the heights are equal across both diagonals of its block, and weight
$1$ when they are equal across one diagonal only (Lemma~\ref{lem:weights}). In height coordinates the
weight is therefore an interaction along the diagonals, not between neighbouring faces.}
\label{fig:vertices}
\end{figure}