A $2$-dimensional affine manifold with singularities $(B,\Delta,\mathscr{A})$ is said to be simple if $\Delta$ consists of a finite union of isolated points and a neighborhood of each $p\in\Delta$ is affine isomorphic to a neighborhood of $0\in\mathbb{R}^{2}$ as in Example 3.7. We call $p\in\Delta$ a node. A $3$-dimensional affine manifold with singularities $(B,\Delta,\mathscr{A})$ is simple if it satisfies:

• (i)

  $\Delta$ is a trivalent graph;

• (ii)

  a neighborhood of each vertex of $\Delta$ is affine isomorphic to a neighborhood of $0\in\mathbb{R}^{3}$ in either Examples 3.10 or 3.11, in which case we call it a positive vertex; or to a neighborhood of $0\in\mathbb{R}^{3}$ in either Examples 3.12 or 3.13, in which case we call it a negative vertex;

• (iii)

  a neighborhood of each edge of the graph is affine isomorphic to a neighborhood of $\Delta$ in Example 3.8; or a neighborhood of $\Delta_{\tau}$ in Example 3.9 for a suitable $\tau$.