  We consider the problem of finding the minimum-weight subgraph that satisfies
given connectivity requirements. Specifically, given a requirement $r \in
\{0,1,2,3\}$ for every vertex, we seek the minimum-weight subgraph that
contains, for every pair of vertices $u$ and $v$, at least $\min\{ r(v),
r(u)\}$ edge-disjoint $u$-to-$v$ paths. We give a polynomial-time approximation
scheme (PTAS) for this problem when the input graph is planar and the subgraph
may use multiple copies of any given edge. This generalizes an earlier result
for $r \in \{0,1,2\}$. In order to achieve this PTAS, we prove some properties
of triconnected planar graphs that may be of independent interest.
