A planar graph is said to be triangulated (also called maximal planar) if the addition of any edge to results in a nonplanar graph.
If the special cases of the triangle graph and tetrahedral graph (which are planar that already contain a maximal number of edges) are included, maximal planar graphs are the skeletons of simple polyhedra and are isomorphic to planar graphs with edges.
Triangulated graphs are implemented in the Wolfram Language as GraphData["Triangulated"].
Apollonian networks are triangulated graphs. The following table summarizes some named triangulated graphs.
The numbers of maximal planar simple graphs on , 2, ... nodes are 0, 0, 1, 1, 1, 2, 5, 14, 50, 233, 1249, ... (OEIS A000109), the first few of which are illustrated above.