The concept of generic polyhedron is closely related to that of special spine in Topology. We remind its definition. Let $M$ be a compact $(n+1)$-manifold with boundary and $\bar{\Pi}\subset M$ be an $n$-dimensional CW-complex such that its every open cell is smoothly embedded to $M$. The complex $\bar{\Pi}$ is called a spine of $M$ if $\bar{\Pi}$ is a deformational retract of $M$. The spine $\bar{\Pi}$ is called special if for any point $x\in\bar{\Pi}\smallsetminus\partial M$ from an open $k$-cell there exists a neighborhood isomorphic to $\mathbb{R}^{k}\times\Sigma^{n-k}$.

Note that if $\operatorname{Int}\Delta\cap\mathbb{Z}^{n+1}=\emptyset$ then all the triangulation vertices of a dual $\Delta$-polyhedron $\Pi$ are from $\partial\Delta$ then $\bar{\Pi}$ is a spine of $\Delta$. In general, $\bar{\Pi}$ is a spine of the polyhedron $\Delta$ minus a small neighborhood of the interior lattice points. Note that $\bar{\Pi}$ can be treated as a special spine of $\Delta$ if we treat $\Delta$ as a manifold with boundary and corners.