P160: Enumeration of all rooted triconnected plane triangulations with at most $n$ vertices

P160: Enumeration of all rooted triconnected plane triangulations with at most $n$ vertices
Input:
An integer $n$.
Output:
All triconnected rooted plane triangulations with at most $n$ vertices.
Complexity:
$O(1)$ time per tree and $O(n)$ space.
Comment:
A \textit{rooted} plane triangulation is a plane triangulation with one designated vertex on the outer face.
Reference:
[Nakano2001] (Bibtex)