diagonal
Let $P$ be a polygon^{} or a polyhedron. Two vertices on $P$ are adjacent^{} if the line segment^{} joining them is an edge of $P$. A diagonal of $P$ is a line segment joining two nonadjacent vertices.
Below is a figure showing a hexagon^{} and all its diagonals (in red) with $X$ as one of its endpoints^{}.
Remarks.

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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} 
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If a polygon $P$ has $n$ (distinct) vertices, then it has $\frac{n(n3)}{2}$ diagonals.
Title  diagonal 

Canonical name  Diagonal 
Date of creation  20130322 17:34:41 
Last modified on  20130322 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 