We focus on the case of a maximally degenerate $K3$ surface $X/K$. We have $C=D_{i_{m}}\cap D_{i_{m^{\prime}}}$, $\Gamma=\{a\}$ is a point in the interior of $\tau_{C}$ and $\gamma$ is a loop around $a$, oriented as the path joining in order $v_{D_{i_{0}}},v_{D_{i_{m}}},v_{D_{i_{\infty}}},v_{D_{i_{m^{\prime}}}}$. We assume we have a retraction $\rho:X^{\an}\longrightarrow\Sk(X)$ such that

$$\rho=\begin{cases}\rho_{\mathscr{X}}&\textrm{ over }\textrm{Int}(\tau_{p_{0}})\cup\textrm{Int}(\tau_{p_{\infty}})\cup[v_{i_{m}},a)\\ \rho_{\mathscr{X}^{\prime}}&\textrm{ over }\textrm{Int}(\tau_{p_{0}})\cup\textrm{Int}(\tau_{p_{\infty}})\cup[v_{i_{m^{\prime}}},a)\end{cases}$$

where $[v_{i_{\cdot}},a)$ is the part of the edge $\tau_{C}$ joining the vertex to $a$, but not including $a$. Then Proposition 3.2.2 may be rewritten as follows.