A facially complete planar embedding is a planar embedding that becomes complete when edges are added for every two vertices that lie on a common face (and do not already correspond to edges in the original embedding). The numbers of 2-connected facially complete planar embeddings for on n vertices for n = 1, 2, ... are given by 0, 0, 1, 3, 6, 15, 32, 94, 295, 1169, 4870, 22110, ... (OEIS A375617; Tiley et al. 2024).

complete graph | cyclic chromatic number | map graph | planar embedding | planar graph