= Vertex cycle of a paired polygon
= Vertex cycles of a paired polygon
{synonym}
A <vertex cycle of a paired polygon> is an equivalence class of vertices under the edge identifications. Its angle sum is the total angle at the resulting point of the quotient surface. Recording the edge labels encountered around that point gives a <group> word, whose order determines the number of turns required to close a lifted cycle. This explains the angle multiplier and lifted vertex count in the <paired-polygon construction of finite surface covers>.
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