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 non-adjacent vertices.

Below is a figure showing a hexagon and all its diagonals (in red) with $X$ as one of its endpoints.

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 $P$.

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• If a polygon $P$ has $n$ (distinct) vertices, then it has ${\displaystyle \frac{n(n-3)}{2}}$ diagonals.