all quadrangulations on 14 vertices.
Plantri only focuses on generating graph embeddings, and for the 3-connected situation, the embedding isomorphism and abstract graph isomorphism are consistent, but for vertex connectivity less than 3, the situation is essentially different. I all generated 15,882 non-isomorphic embeddings of quadrangulations on 14 vertices by plantri. Further elimination of abstract isomorphic graphs is then necessary.
A total of 14805 non-isomorphic quadrangulations on 14 vertices were screened out.
See relevant links.
https://math.stackexchange.com/questions/4635964/all-quadrangulations-on-14-vertices
We can combine plantri with nauty to find the set of 14805 graphs: ./plantri 14 -q -c2m2 -g | ./nauty/shortg