A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing,"
of a planar graph is an embedding in which no two
edges intersect (or overlap) and no two vertices coincide. Equivalently, a planar
embedding is an embedding of a graph drawn in the plane such that edges intersect
only at their endpoints.

The numbers of embeddings on the sphere of 2-connected planar graphs with , 2, ... nodes are given by 0, 0, 1, 3, 10, 61, 564, 7593,
123874, ... (OEIS A034889). The first case
where this exceeds the number of nonisomorphic 2-connected planar graphs occurs for
, where a single 5-vertex planat graph
has two distinct planar embeddings on the sphere.

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Harborth, H. and Möller,
M. "Minimum Integral Drawings of the Platonic Graphs." Math. Mag.67,
355-358, 1994.Sloane, N. J. A. Sequence A034889
in "The On-Line Encyclopedia of Integer Sequences."