Topological graph theory

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 may be denoted .It can be obtained from a signed rotation system or ribbon graph representation of the embedding by twisting every edge of the embedding. (Wikipedia).

Petrie dual
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Related pages

Dual graph | Manifold | Petrie polygon | Ribbon graph | Decagon | Decagram (geometry) | Regular polyhedron | Bipartite graph | Topological graph theory | Order-4 hexagonal tiling | Rotation system | Skew polygon | Euler characteristic | Graph embedding | Hexagonal tiling | Regular dodecahedron | Regular map (graph theory) | Wilson operation