  We explicitly construct a collection of bad 3-orbifolds, \(\mathcal{X}\),
satisfying the following properties:
  \begin{enumerate}
  \item The underlying topological space of any \(X \in \mathcal{X}\) is
homeomorphic to $S^2\times I$ or $(S^2\times S^1)\backslash B^3$.
  \item The boundary of any \(X \in \mathcal{X}\) consists of one or two
spherical 2-orbifolds.
  \item Any bad 3-orbifold is obtained from a good 3-orbifold by repeating,
finitely many times, the following operation: remove one or two orbifold-balls,
and glue in some \(X \in \mathcal{X}\).
  \end{enumerate}
  Conversely, any bad 3-orbifold \(\OO\) contains some \(X \in \mathcal{X}\) as
a sub-orbifold; we call removing \(X\) and capping the resulting boundary \em
cut-and-cap.\em\ Then by cutting-and-capping finitely many times we obtain a
good orbifold.
