diagonal
Let be a polygon or a polyhedron. Two vertices on are adjacent if the line segment joining them is an edge of . A diagonal of is a line segment joining two non-adjacent vertices.
Remarks.
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If is convex, then the relative interior of a diagonal lies in the relative interior of . Below is a figure showing that a diagonal may partially lie outside of .
\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 has (distinct) vertices, then it has diagonals.
Title | diagonal |
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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 |