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In topological graph theory, the Petrie dual of an embedded graph 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 }}.It can be obtained from a signed rotation system or ribbon graph representation of the embedding by twisting every edge of the embedding.
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