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About: Petrie dual     Goto   Sponge   NotDistinct   Permalink

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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.