Let $B$ and $\Delta$ be as in Example 3.10. Clearly, $\mathbb{R}^{2}-\Delta$ has three connected components, which we denote $C_{1},C_{2}$ and $C_{3}$. Let $\bar{C}_{j}=C_{j}\cup\partial C_{j}$. Viewing $\mathbb{R}^{2}$ embedded in $B$ as $\{0\}\times\mathbb{R}^{2}$, consider the following three open subsets of $B_{0}$:

	$\displaystyle U_{1}$	$\displaystyle=$	$\displaystyle\mathbb{R}^{3}-(\bar{C}_{2}\cup\bar{C}_{3}),$
	$\displaystyle U_{2}$	$\displaystyle=$	$\displaystyle\mathbb{R}^{3}-(\bar{C}_{1}\cup\bar{C}_{3}),$
	$\displaystyle U_{3}$	$\displaystyle=$	$\displaystyle\mathbb{R}^{3}-(\bar{C}_{1}\cup\bar{C}_{2}).$

Let

	$\displaystyle V^{+}$	$\displaystyle=$	$\displaystyle\{x_{1}>0\},$
	$\displaystyle V^{-}$	$\displaystyle=$	$\displaystyle\{x_{1}<0\}.$

Clearly $U_{i}\cap U_{j}=V^{+}\cup V^{-}$ when $i\neq j$. If $T_{1}$ and $T_{2}$ are as in (9), define the following coordinate charts on $U_{1}$, $U_{2}$, $U_{3}$ respectively:

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

We can check that the affine structure defined by these charts is such that, for fixed $b\in B_{0}$, there exists a basis of $T^{\ast}_{b}B_{0}$ with respect to which the holonomy representation is such that $\rho^{\ast}(g_{j})=T_{j}$, where $g_{j}$ are as in Figure 3. In particular, the holonomy is given by the inverse transpose matrices of the holonomy in the previous example.