Editing Decagon (section)

===Construction===
As 10 = 2 × 5, a [[power of two]] times a [[Fermat prime]], it follows that a regular decagon is [[constructible polygon|constructible]] using [[compass and straightedge]], or by an edge-[[bisection]] of a regular [[pentagon]].<ref name="ludlow">{{citation|title=Geometric Construction of the Regular Decagon and Pentagon Inscribed in a Circle|first=Henry H.|last=Ludlow|publisher=The Open Court Publishing Co.|year=1904|url=https://books.google.com/books?id=vLMlw7uL8kgC}}.</ref>
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| image1 = Regular Decagon Inscribed in a Circle.gif
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| caption1 = Construction of decagon
| image2 = Regular Pentagon Inscribed in a Circle.gif
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| caption2 = Construction of pentagon
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An alternative (but similar) method is as follows:
#Construct a pentagon in a circle by one of the methods shown in [[Pentagon#Construction of a regular pentagon|constructing a pentagon]].
#Extend a line from each vertex of the pentagon through the center of the [[circle]] to the opposite side of that same circle. Where each line cuts the circle is a vertex of the decagon.  In other words,  [[Image (mathematics)#Image_of_a_subset|the image]] of a regular pentagon under a [[point reflection]] with respect of [[Regular polygon#Symmetry|its center]] is a [[Concentric objects|concentric]] ''[[Congruence (geometry)|congruent]]'' pentagon,  and the two pentagons have in total the vertices of a concentric ''regular decagon''.
#The five corners of the pentagon constitute alternate corners of the decagon. Join these points to the adjacent new points to form the decagon.