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It is always hard to draw a polygon (eg. decagons, nonagons, heptagons...etc) with compass and ruler. The method I discovered is to divide a polygon into smaller triangles.  That means you only have to concentrate on one intersected triangle and the relations between the vectors. The other triangles are just repetitions.

Your challenge is how to find out the angle phi for other n-polygons (general knowledge: Trigonometry, Maths - Secondary School). I give you a hint in the following pdf for n-gons. 


If you have the solution for phi, don't post it here, they have to solve for their own! 

So let's get started how to fold the pentagon.
   

Step 1: The Crease Pattern

Red: valley folds
Blue: mountain folds
Black: cutting lines

Step 2: Cut, Precrease and Glue

So the next step is to precrease everything and to glue it to a ring. (in the middle there are 6 rectangles, one is for gluieng, overlap the first rectangle with the last one)

Step 3: Fold and Tuck

The next step is to fold and tuck the precreased paper ring into a pentagon. Repeat it for the another side.

Step 4: The Result

And you are finished

Happy Folding!
<p>guys iam a 10th grade student. i really dont understand ur math up there so pls help</p>
Too easy!!! And super awesome!!
cool
Great instructable! This is really cool.
WOW, yours is a very useful discovering!
Thanks :)

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Bio: Nowadays attempting creating small apps to dive into the world of programming and Software Development
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