Dual polygon

In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.

In a cyclic polygon, longer sides correspond to larger exterior angles in the dual (a tangential polygon), and shorter sides to smaller angles.

As an example of the side-angle duality of polygons we compare properties of the cyclic and tangential quadrilaterals.

From the point of view of the dual curve, where to each point on a curve one associates the point dual to its tangent line at that point, the projective dual can be interpreted thus: Combinatorially, one can define a polygon as a set of vertices, a set of edges, and an incidence relation (which vertices and edges touch): two adjacent vertices determine an edge, and dually, two adjacent edges determine a vertex.

Then the dual polygon is obtained by simply switching the vertices and edges.