dual_planar_diagram

dual_planar_diagram(k: PlanarDiagram) → PlanarDiagram

Generates the dual of a given planar diagram by transforming its structure such that nodes of the dual correspond to faces in the original diagram, and edges represent adjacency relationships between those faces.

The function takes a PlanarDiagram object, constructs its dual by iterating through its faces and endpoints, and establishes the adjacency relationships in the dual. The dual diagram’s name is updated to reflect its dual nature if the original diagram has a name.

Args:

k (PlanarDiagram): The planar diagram whose dual is to be generated.

Returns:

PlanarDiagram: The dual planar diagram of the given input diagram.