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| {{refimprove|date=August 2012}}
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| {{Even polygon db|Even polygon stat table|p20}}
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| In [[geometry]], an '''icosagon''' is a twenty-sided [[polygon]]. The sum of any icosagon's interior angles is 3240 degrees.
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| One interior angle in a [[regular polygon|regular]] icosagon is 162°, meaning that one exterior angle would be 18°.
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| The regular icosagon is a [[constructible polygon]], by an edge-[[bisection]] of a regular [[decagon]], and can be seen as a [[Truncation (geometry)|truncated]] decagon.
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| ==Regular Icosagon==
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| The [[area]] of a regular icosagon is: (with ''t'' = edge length)
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| :<math>A={5}t^2(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}) \simeq 31.56875757 t^2.</math>
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| ==Uses==
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| The Big Wheel on the popular US game show ''[[The Price Is Right (US game show)|The Price Is Right]]'' is an icosagon.
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| The Globe, the outdoor theater used by William Shakespeare's acting company, was discovered to have been built on an icosagonal foundation when a partial excavation was done in 1989.<ref> [http://researchmagazine.uga.edu/92f/globe.html]</ref>
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| As a [[golygon]]al path, the [[swastika]] is considered to be an irregular icosagon.<ref>{{MathWorld |title=Icosagon |urlname=Icosagon}}</ref>
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| [[File:4.5.20 vertex.png|160px]]
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| A regular square, pentagon, and icosagon can completely fill a plane vertex.
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| ===Construction=== | |
| A regular icosagon is [[constructible polygon|constructible]] using a [[compass and straightedge]]:
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| [[File:Regular Icosagon Inscribed in a Circle.gif]]<BR>Construction of a regular icosagon
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| ===Petrie polygons===
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| The regular icosagon is the [[Petrie polygon]] for a number of higher dimensional polytopes, shown in [[orthogonal projection]]s in [[Coxeter plane]]s:
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| {| class=wikitable
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| |- align=center
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| !valign=center|A<sub>9</sub>
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| |[[File:19-simplex_t0.svg|100px]]<br>[[19-simplex]] (19D)
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| |- align=center valign=top
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| !valign=center|BC<sub>10</sub>
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| |[[File:10-cube_t9.svg|100px]]<br>[[10-orthoplex]]
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| |[[File:10-cube_t8.svg|100px]]<br>[[Rectified 10-orthoplex]]
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| |[[File:10-cube_t7.svg|100px]]<br>[[Birectified 10-orthoplex]]
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| |[[File:10-cube_t6.svg|100px]]<br>[[Trirectified 10-orthoplex]]
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| |[[File:10-cube_t5.svg|100px]]<br>[[Quadrirectified 10-orthoplex]]
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| |[[File:10-cube_t4.svg|100px]]<br>[[Quadrirectified 10-cube]]
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| |[[File:10-cube_t3.svg|100px]]<br>[[Trirectified 10-cube]]
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| |[[File:10-cube_t2.svg|100px]]<br>[[Birectified 10-cube]]
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| |[[File:10-cube_t1.svg|100px]]<br>[[Rectified 10-cube]]
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| |- align=center valign=top
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| !valign=center|D<sub>11</sub>
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| |[[File:11-demicube.svg|100px]]<br>[[11-demicube]]
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| |- align=center valign=top
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| !valign=center|E<sub>8</sub><br>[20]
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| |[[File:4_21_t0_p20.svg|100px]]<br>[[4 21 polytope|(4<sub>21</sub>)]]
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| |[[File:4_21_t1_p20.svg|100px]]<br>t<sub>1</sub>(4<sub>21</sub>)
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| |[[File:4_21_t2_p20.svg|100px]]<br>t<sub>2</sub>(4<sub>21</sub>)
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| |[[File:4_21_t3_p20.svg|100px]]<br>t<sub>3</sub>(4<sub>21</sub>)
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| |[[File:4_21_t4_p20.svg|100px]]<br>t<sub>4</sub>(4<sub>21</sub>)
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| |[[File:2_41_t0_p20.svg|100px]]<br>t<sub>0</sub>(2<sub>41</sub>)
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| |[[File:2_41_t1_p20.svg|100px]]<br>t<sub>1</sub>(2<sub>41</sub>)
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| |[[File:1_42_t0_p20.svg|100px]]<br>t<sub>0</sub>(1<sub>42</sub>)
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| |- align=center valign=top
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| !valign=center|H<sub>4</sub><br>[20]
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| |[[File:600-cell_t1_p20.svg|100px]]<br>[[Rectified 600-cell]]
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| |[[File:600-cell_t0_p20.svg|100px]]<br>[[600-cell]]
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| |}
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| ==References==
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| {{Reflist}}
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| *[http://mathforum.org/dr.math/faq/faq.polygon.names.html Naming Polygons and Polyhedra]
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| {{Clear}}
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| {{polygons}}
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| [[Category:Polygons]]
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