= Plane tree
A <plane tree> is a <tree> embedded in an oriented plane, with the embedding considered up to deformation preserving the cyclic order of incident <edges>. The cyclic order distinguishes plane embeddings that an abstract <graph isomorphism> can forget.
After choosing a root, the parent <edge> gives a starting position for the children at each nonroot <vertex>. At the root there is no parent <edge>: a marked root corner is needed to turn its cyclic order into a linear child order. A <rooted plane tree> includes that extra choice, equivalently an ordered child list at every vertex. Merely distinguishing the root vertex does not select its first child.
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