A planar embedding of a topological space 
is a map 
into the Euclidean
plane that is a homeomorphism from 
onto its image with the relative
topology.
In graph theory, a planar graph embedding represents vertices by distinct points and edges by arcs meeting only at common endpoints. A connected graph embedded in this way, together with its faces, determines a planar map.
Planar embeddings are also studied for other topological spaces, including continua (Anušić et al. 2020). Embedding the graph of a simplicial complex does not necessarily embed the whole simplicial complex. For example, the boundary of a tetrahedron has a planar graph as its 1-skeleton, but the whole boundary is a sphere and cannot be embedded in the plane.
