What's the name of a planar graph in which every (inner) face has the same number $k$ of vertices? Something like $k$-uniform planar graph?
And is there a name for planar graphs in which every face has at most $k$ vertices?
If $k=3$ you call the graph a triangulation. If $k=4$ it is called quadrangulation. I am not aware of any other terms for a fixed $k>4$.
For a non-fixed $k$ you might say graphs with face-degree $k$. Or duals of $k$-regular graphs. How about $k$-gonalization?