Petrie dual
In topological graph theory, the Petrie dual of an embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie polygons of the first embedding as its faces. The Petrie dual is also called the petrial, and the Petrie dual of an embedded graph G {\displaystyle G} may be denoted G π {\displaystyle G^{\pi }} .