Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A closed plane figure bounded by three or more line segments.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A plane figure bounded by straight edges.
 n. The boundary of such a figure.
 n. A figure comprising vertices and (not necessarily straight) edges, alternatingly.
 n. Such a figure and its interior, taken as a whole.
from the GNU version of the Collaborative International Dictionary of English
 n. A plane figure having many angles, and consequently many sides; esp., one whose perimeter consists of more than four sides; any figure having many angles.
from The Century Dictionary and Cyclopedia
 n. In geometry, a closed figure formed by the intersections of a number of straight lines, each with two others; especially, a plane figure of this sort; a figure with numerous angles
 n. two sets of n lines, each cutting all the lines of the other set upon one curve of the nth order.
 n. A train of sects whose last point is identical with the first.
 n. In ordnance, a place especially arranged for making ballistic tests of guns, projectiles, armor, and powder. Same as provingground.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a closed plane figure bounded by straight sides
Etymologies
Examples

His mathematical friends could have told him, that though it was talked of as a polygon, it was not supposed to be a square; but _polygon_ would not have rhymed to _stare_; and poets, when they launch into the ocean of words, must have an eye to the helm; at all events a poet, who is not supposed to be a student of the exact sciences, may be forgiven for a mathematical blunder.

The term polygon is applied to figures having flat sides equidistant from a common centre.

Measuring Po by admin on Jul. 03, 2009, under Uncategorized the measure of an exterior angle of a regular polygon is 30 degrees.

How many diagonals can be drawn in the po? the measure of an exterior angle of a regular polygon is 30 degrees.

When an Englishspeaking child is confronted for the first time with the word polygon, he needs an explanation.

He took the circle to be an infinilateral regular polygon, that is, a regular polygon with an infinite number of (infinitesimally short) sides.

You can see here on the radar screen, this pink polygon, that is where that tornado warning is for northwest Alabama and the cell itself really, really weakening here.

This is the purple polygon, which is a part of the county near Driscoll, which is affected by this.

And this polygon, which is a new way that we indicate severe weather warnings out of the National Weather Service, kind of zooms it in and narrows it down just a little bit.

The next step is to see where the meteorological stations are and the assign each station an area of influence defined as a polygon whose boundary is the 1/2 way point between adjacent stations, old fashioned way of doing polygonised ore reserves so that we end up each station having an area assigned to it.
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oroboros commented on the word polygon
When your parrot flies the coop?
January 14, 2011