Diagonal

A diagonal is a line segment joining two nonadjacent vertices of a polygon or polyhedron. In a polygon, it lies inside the shape.

Polygon: A closed plane figure formed by a finite sequence of straight line segments. A polygon's vertices and edges establish which pairs are nonadjacent.
Diagonal count: The number of diagonals in a polygon with a given number of vertices. The formula follows by counting possible vertex pairs and removing sides.
Polygon triangulation: A partition of a polygon into triangles by drawing noncrossing diagonals between its vertices. It uses diagonals to reduce polygon problems to simpler triangular pieces.
Side (geometry): A boundary segment of a polygon connecting consecutive vertices. A side joins adjacent vertices, whereas a diagonal joins nonadjacent ones.
Vertex: A point where two or more lines, edges, or rays meet. A diagonal connects a pair of polygon or polyhedron vertices.
Binomial coefficient: The number of ways to choose a fixed-size subset from a finite set. Choosing two vertices gives the total candidate segments before boundary edges are excluded.
Planar graph: A graph drawable in the plane with edges meeting only at shared endpoints. Polygon diagonals create additional edges while remaining within the polygon's planar drawing.
Face diagonal: A diagonal lying in one polygonal face of a polyhedron. It contrasts with a space diagonal, which passes through the polyhedron's interior.
Edge (geometry): A line segment forming the boundary of a polygon or polyhedron. Unlike an edge, a diagonal joins vertices that are not neighbors along the boundary.
Complete graph: A graph in which every pair of distinct vertices is connected by an edge. Its edges represent all possible vertex pairs, including polygon sides and diagonals.

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