How to Construct a Regular Heptagon

Last Updated: June 14, 2022

A regular heptagon (also called septagon) is a polygon with seven equal sides and seven equal angles. Accurately constructing polygons is an important part of geometry, and for regular heptagons there are multiple ways to draw one. Here is the easiest method if you are using a straight edge and compass.

Steps

1
Draw an arbitrary circle, centred at a point $X$ . Keep in mind that you will need some extra space around the circle for construction lines.^{[1]
X
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2
Draw the radius $AX$ .^{[2]
X
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3
Draw a circle with radius $AX$ , centred at $A$ . This circle intersects the first circle at points $B$ and $C$ .^{[3]
X
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4
Connect $B$ and $C$ . $BC$ bisects $AX$ in $E$ .^{[4]
X
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5
Draw a third circle with radius $BE$ , centred at $B$ . This circle intersects circle a in $D$ .^{[5]
X
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6
Use your compass to trace the distance BD around the circle. You should end up exactly where you started. There is an error of about .2% for this method, which is negligible for any heptagon that fits on a regular A4 piece of paper. If you don't end up exactly where you started, there were probably some inaccuracies with the construction tools (e.g. the thickness of the pencil).^{[6]
X
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7
Connect adjacent vertices.
8
Erase the construction lines if needed.

Community Q&A

Question

How do I build a pentagon?

Donagan

Top Answerer

See Construct a Regular Pentagon.

Warnings

Since 7 cannot be written as the product of a power of two and a Fermat prime, it is impossible to do an exact compass and straightedge construction of a heptagon. However, the above method has an error of less than 0.2%. When the circumscribed circle of the heptagon has a radius of 1 meter, there will be an error of approx. 1.7 mm.

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