Let P be a polygonMathworldPlanetmathPlanetmath or a polyhedron. Two vertices on P are adjacentPlanetmathPlanetmathPlanetmath if the line segmentMathworldPlanetmath joining them is an edge of P. A diagonal of P is a line segment joining two non-adjacent vertices.

Below is a figure showing a hexagonMathworldPlanetmath and all its diagonals (in red) with X as one of its endpointsMathworldPlanetmath.


  • If P is convex, then the relative interior of a diagonal lies in the relative interior of P. Below is a figure showing that a diagonal may partially lie outside of P.

    \begin{pspicture}(-227.62204pt,0.0pt)(0.0pt,56.905502pt)\leavevmode% \ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces% \ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces% \ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces% \special{pst: \pst@dict\tx@STP\pst@newpath\psk@origin\psk@swapaxes\pst@code end }\ignorespaces\leavevmode\ignorespaces\ignorespaces\ignorespaces\ignorespaces% \special{pst: \pst@dict\tx@STP\pst@newpath\psk@origin\psk@swapaxes\pst@code end }\ignorespaces\end{pspicture}
  • If a polygon P has n (distinct) vertices, then it has n(n-3)2 diagonals.

Title diagonal
Canonical name Diagonal
Date of creation 2013-03-22 17:34:41
Last modified on 2013-03-22 17:34:41
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 51N05
Related topic BasicPolygon
Related topic Polyhedron
Defines adjacent vertices