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| {{unreferenced|date=August 2012}}
| | Andrew Berryhill is what his wife enjoys to call him and he totally digs that title. To climb is something she would by no means give up. For years she's been operating as a travel agent. Her family lives in Alaska but her spouse wants them to move.<br><br>Also visit my web blog ... free psychic reading ([http://myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ http://myoceancounty.net]) |
| {{Even polygon db|Even polygon stat table|p16}}
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| In mathematics, a '''hexadecagon''' (sometimes called a hexakaidecagon) is a [[polygon]] with 16 [[Edge (geometry)|sides]] and 16 [[Vertex (geometry)|vertices]].<ref name=Weisstein2002>{{cite book|last=Weisstein|first=Eric W.|title=CRC Concise Encyclopedia of Mathematics, Second Edition|year=2002|publisher=CRC Press|isbn=9781420035223|page=1365}}</ref>
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| ==Regular hexadecagon==
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| A regular hexadecagon is [[constructible polygon|constructible]] with a [[Compass and straightedge constructions|compass and straightedge]].
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| Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees.
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| ===Construction===
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| A regular hexadecagon is [[constructible polygon|constructible]] using [[compass and straightedge]]:
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| [[File:Regular_Hexadecagon_Inscribed_in_a_Circle.gif]]<br>Construction of a regular hexadecagon
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| ==Area==
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| The [[area]] of a regular hexadecagon is: (with ''t'' = edge length)
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| :<math>A = 4t^2 \cot \frac{\pi}{16} = 4t^2 (\sqrt{2}+1)(\sqrt{4-2\sqrt{2}}+1)</math>
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| Because the hexadecagon has a number of sides that is a [[power of two]], its area can be computed in terms of the [[circumradius]] ''r'' by truncating [[Viète's formula]]:
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| :<math>A=r^2\cdot\frac{2}{1}\cdot\frac{2}{\sqrt{2}}\cdot\frac{2}{\sqrt{2+\sqrt{2}}}=4r^2\sqrt{2-\sqrt{2}}.</math>
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| ===Petrie polygons===
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| The regular hexadecagon is the [[Petrie polygon]] for many higher dimensional polytopes, shown in these skew [[orthogonal projection]]s, including:
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| {| class=wikitable width=80
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| |- align=center valign=top
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| !valign=center|A<sub>15</sub>
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| |[[File:15-simplex_t0.svg|100px]]<br>[[15-simplex]]
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| |- align=center valign=top
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| !valign=center|B<sub>8</sub>
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| |[[File:8-cube_t7.svg|100px]]<br>[[8-orthoplex]]
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| |[[File:8-cube_t6.svg|100px]]<br>[[Rectified 8-orthoplex]]
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| |[[File:8-cube_t5.svg|100px]]<br>[[Birectified 8-orthoplex]]
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| |[[File:8-cube_t4.svg|100px]]<br>[[Trirectified 8-orthoplex]]
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| |[[File:8-cube_t3.svg|100px]]<br>[[Trirectified 8-cube]]
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| |[[File:8-cube_t2.svg|100px]]<br>[[Birectified 8-cube]]
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| |[[File:8-cube_t1.svg|100px]]<br>[[Rectified 8-cube]]
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| |[[File:8-cube_t0.svg|100px]]<br>[[8-cube]]
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| |- align=center valign=top
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| !valign=center|D<sub>9</sub>
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| |[[File:9-cube_t8_B8.svg|100px]]<br>[[9-orthoplex|t<sub>7</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t7_B8.svg|100px]]<br>[[rectified 9-orthoplex|t<sub>6</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t6_B8.svg|100px]]<br>[[birectified 9-orthoplex|t<sub>5</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t5_B8.svg|100px]]<br>[[trirectified 9-orthoplex|t<sub>4</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t4_B8.svg|100px]]<br>[[quadrirectified 9-cube|t<sub>3</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t3_B8.svg|100px]]<br>[[trirectified 9-cube|t<sub>2</sub>(1<sub>61</sub>)]]
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| |[[File:9-cube_t2_B8.svg|100px]]<br>[[birectified 9-cube|t<sub>1</sub>(1<sub>61</sub>)]]
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| |[[File:9-demicube.svg|100px]]<br>[[9-demicube]]<br>(1<sub>61</sub>)
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| |}
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| ==References==
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| {{reflist}}
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| ==External links==
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| *{{MathWorld|title=Hexadecagon|urlname=Hexadecagon}}
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| {{Polygons}}
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| [[Category:Polygons]]
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Andrew Berryhill is what his wife enjoys to call him and he totally digs that title. To climb is something she would by no means give up. For years she's been operating as a travel agent. Her family lives in Alaska but her spouse wants them to move.
Also visit my web blog ... free psychic reading (http://myoceancounty.net)