Petrie dual
http://dbpedia.org/resource/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.
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在中，嵌入圖的皮特里對偶（Petrie Dual）是指所有面皆為2-流形盤面之的另一種，且是含有前述嵌入圖之嵌入对象的皮特里多邊形作為維面的圖嵌入。皮特里對偶亦可以作為一種多面體變換，稱為皮特里變換（Petrie Operation），其會將原像的面以皮特里多邊形做替換，然而變換結果通常會因為面轉變為無法確定唯一封閉區域的皮特里多邊形而導致體積與表面積不存在。 若原像計為，則變換結果可以用表示。
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Petrie dual
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皮特里對偶
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right
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The Petrie polygon of the dodecahedron is a skew decagon. Seen from the solid's 5-fold symmetry axis it looks like a regular decagon. Every pair of consecutive sides belongs to one pentagon .
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Skeleton 12, Petrie, stick, size l, 5-fold.png
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Skeleton 12, Petrie, stick, size l.png
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500
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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.
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在中，嵌入圖的皮特里對偶（Petrie Dual）是指所有面皆為2-流形盤面之的另一種，且是含有前述嵌入圖之嵌入对象的皮特里多邊形作為維面的圖嵌入。皮特里對偶亦可以作為一種多面體變換，稱為皮特里變換（Petrie Operation），其會將原像的面以皮特里多邊形做替換，然而變換結果通常會因為面轉變為無法確定唯一封閉區域的皮特里多邊形而導致體積與表面積不存在。 若原像計為，則變換結果可以用表示。
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8619
