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decagon

 
Dictionary: dec·a·gon   (dĕk'ə-gŏn') pronunciation
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decagon
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decagon
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n.
A polygon with ten angles and ten sides.

[Medieval Latin decagōnum, from Greek dekagōnon, from neuter of dekagōnos, having ten angles : deka, ten + -gōnos, angled; see -gon.]

decagonal de·cag'o·nal (dĭ-kăg'ə-nəl) adj.
decagonally de·cag'o·nal·ly adv.

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WordNet: decagon
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Note: click on a word meaning below to see its connections and related words.

The noun has one meaning:

Meaning #1: a polygon with 10 sides and 10 angles

Wikipedia: Decagon
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Regular decagon
Regular decagon.svg
Edges and vertices 10
Schläfli symbols {10}
t{5}
Coxeter–Dynkin diagrams CDW ring.pngCDW 10.pngCDW dot.png
CDW ring.pngCDW 5.pngCDW ring.png
Symmetry group Dihedral (D10)
Area
(with t=edge length)		 A = \frac{5}{2}t^2 \cot \frac{\pi}{10} = \frac{5t^2}{2} \sqrt{5+2\sqrt{5}} \simeq 7.694208843 t^2.
Internal angle
(degrees)		 144°
Properties convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and all internal angles equal to 144°. Its Schläfli symbol is {10}.

Contents

Construction

A regular decagon is constructible with a compass and straightedge.

  1. Complete steps 1 through 6 of constructing a pentagon.
  2. Extend a line from each corner of the pentagon through the center of the circle made in step 1 of constructing a pentagon to the opposite side of that same circle. If you cut the angles off the pentagon you will get the shape of a decagon
  3. The five corners of the pentagon constitute every other corner of the decagon. The remaining five corners of the decagon are those points where the lines of step 2 cross the original circle (but not a pentagon corner).

Petrie polygons

The regular decagon is the Petrie polygon for six higher dimensional polytopes, shown in these skew orthogonal projections:

Dodecahedron petrie.png
Dodecahedron (3D)		 Icosahedron petrie.png
Icosahedron (3D)		 Cross graph 5.svg
5-orthoplex (8D)
Penteract ortho petrie.svg
5-cube (8D)		 Demihexeract ortho petrie.svg
6-demicube (9D)		 Complete graph K10.svg
9-simplex (9D)

See also

External links

v • d • e
Polygons
Listed by number of sides
1–10 sides
11–20 sides
Star polygons
Stub icon This geometry-related article is a stub. You can help Wikipedia by expanding it.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Translations: Decagon
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Dansk (Danish)
n. - tisidet figur

Nederlands (Dutch)
tienhoek

Français (French)
n. - (Géom) décagone

Deutsch (German)
n. - Zehneck

Ελληνική (Greek)
n. - δεκάγωνο

Italiano (Italian)
decagono

Português (Portuguese)
n. - decágono (m)

Русский (Russian)
десятиугольник

Español (Spanish)
n. - decágono

Svenska (Swedish)
n. - tiohörning

中文（简体）(Chinese (Simplified))
十边形, 十角形

中文（繁體）(Chinese (Traditional))
n. - 十邊形, 十角形

한국어 (Korean)
n. - 10각형

日本語 (Japanese)
n. - 十辺形, 十角形

العربيه (Arabic)
‏(الاسم) شكل بعشرة زوايا وجوانب‏

עברית (Hebrew)
n. - ‮בעל עשר צלעות, מעושר‬

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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
WordNet. WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Decagon".  Read more
Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved.  Read more