The diameter of a polygon is the largest distance between any pair of its vertices . The vertices
need not be nonadjacent, so this distance may be the
length of a side or a polygon
diagonal . This definition does not require the polygon
to have a circumcircle .
For a regular polygon with sides and circumradius
(1)
Thus an odd-sided regular polygon has a diameter
shorter than the diameter of its circumcircle .
See also Biggest Little Polygon ,
Diameter ,
Generalized
Diameter ,
Graham's Biggest Little
Hexagon ,
Graph Diameter ,
Polygon
Diagonal ,
Polygon Vertex
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References Audet, C.; Hansen, P.; Messine, F.; and Perron, S. "The Minimum Diameter Octagon with Unit-Length Sides: Vincze's Wife's Octagon Is Suboptimal."
J. Combin. Th. Ser. A 108 , 63-75, 2004. Referenced on Wolfram|Alpha Polygon Diameter
Cite this as:
Weisstein, Eric W. "Polygon Diameter."
From MathWorld https://mathworld.wolfram.com/PolygonDiameter.html
Subject classifications
sides and circumradius 
, the diameter is
