  In this paper we give a detailed proof that the Milnor fiber $X_t$ of an
analytic complex isolated singularity function defined on a reduced
$n$-equidimensional analytic complex space $X$ is a regular neighborhood of a
polyhedron $P_t \subset X_t$ of real dimension $n-1$. Moreover, we describe the
degeneration of $X_t$ onto the special fiber $X_0$, by giving a continuous
collapsing map $\Psi_t: X_t \to X_0$ which sends $P_t$ to $\{0\}$ and which
restricts to a homeomorphism $X_t \backslash P_t \to X_0 \backslash \{0\}$.
