Take $B=\mathbb{R}\times\mathbb{R}^{2}$, with coordinates $(x_{1},x_{2},x_{3})$ and identify $\mathbb{R}^{2}$ with $\{0\}\times\mathbb{R}^{2}$. Inside $\mathbb{R}^{2}$ consider the cone over three points:

$$\Delta=\{x_{2}=0,\,x_{3}\leq 0\}\cup\{x_{3}=0,\,x_{2}\leq 0\}\cup\{x_{2}=x_{3},\,x_{3}\geq 0\}.$$

Now define closed sets in $B$

	$\displaystyle R$	$\displaystyle=$	$\displaystyle\mathbb{R}\times\Delta,$
	$\displaystyle R^{+}$	$\displaystyle=$	$\displaystyle\mathbb{R}_{\geq 0}\times\Delta,$
	$\displaystyle R^{-}$	$\displaystyle=$	$\displaystyle\mathbb{R}_{\leq 0}\times\Delta,$

and consider the following cover $\{U_{i}\}$ of $\mathbb{R}^{3}-\Delta$:

	$\displaystyle U_{1}$	$\displaystyle=$	$\displaystyle\mathbb{R}^{3}-R^{+},$
	$\displaystyle U_{2}$	$\displaystyle=$	$\displaystyle\mathbb{R}^{3}-R^{-}.$

It is clear that $U_{1}\cap U_{2}$ has the following three connected components

	$\displaystyle V_{1}$	$\displaystyle=$	$\displaystyle\{x_{2}<0,\ x_{3}<0\},$
	$\displaystyle V_{2}$	$\displaystyle=$	$\displaystyle\{x_{2}>0,\ x_{2}>x_{3}\},$
	$\displaystyle V_{3}$	$\displaystyle=$	$\displaystyle\{x_{3}>0,\ x_{3}>x_{2}\}.$

Take two matrices

$$T_{1}=\left(\begin{array}[]{ccc}1&1&0\\ 0&1&0\\ 0&0&1\end{array}\right),\ \ \ T_{2}=\left(\begin{array}[]{ccc}1&0&-1\\ 0&1&0\\ 0&0&1\end{array}\right).$$

(9)

Now on $U_{1},U_{2}$ we define coordinate maps $\phi_{1}$, $\phi_{2}$ as follows

	$\displaystyle\phi_{1}$	$\displaystyle=$	$\displaystyle\I,$
	$\displaystyle\phi_{2}$	$\displaystyle=$	$\displaystyle\left\{\begin{array}[]{ll}\I&\text{on}\ \bar{V}_{1}\cap U_{2},\\ T_{1}^{-1}&\text{on}\ \bar{V}_{2}\cap U_{2}\\ T_{2}&\text{on}\ \bar{V}_{3}\cap U_{2}\end{array}\right.$

Again we see that $\mathscr{A}=\{U_{i},\phi_{i}\}_{i=1,2}$ gives an affine structure on $B_{0}=\mathbb{R}^{3}-\Delta$. One can compute that given a point $b\in B_{0}$ and closed paths $g_{1}$, $g_{2}$ and $g_{3}$ as in Figure 3, we can choose a basis of $T^{\ast}_{b}B_{0}$ with respect to which the holonomy matrices satisfy $\rho^{\ast}(g_{j})=(T_{j}^{-1})^{t}$ for $j=1,2,3$.