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Homediagonal
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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.
(8,0)(0,3) \pspolygon(5,0)(3,0)(2,1.4)(3,3)(5,3)(6,1.5) \psline[linecolor=red](6,1.5)(3,0) \psline[linecolor=red](3,0)(3,3) \psline[linecolor=red](3,0)(5,3) \rput[b](2.7,0.3)$X$ \rput[l](6,1.5). \rput[a](3,3). \rput[r](2,1.4).
Remarks.

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 $P$.
\pspicture(8,0)(0,2) \pspolygon(5,0)(4,0.5)(2,0)(2,2)(3,1)(4,1.3)(5,1.3)(6,2)(6,0.7) \psline[linecolor=red](6,0.7)(2,2)

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