YouTube video: http://youtu.be/UcjmB_urZQ8

I have used the following method to draw polygons in my Graph-O-Doodle app and wanted to make a simple version to show you.
The method to draw a polygon centers on three basic steps:
- draw a line
- turn an angle
- check if we are back at the starting point
That's it in a nutshell.
Of course the implementation of this is a but more involved.
I have placed comments on each procedure, variable declaration and event to explain what it's purpose is.
By changing the angle used to make each drawing in this project, you can see a progression of alternating spiraling figures and simple polygons.
Take a triangle.
Each angle is 60 degrees.
Vary that by one degree and you get either a left or right spiraling pattern that resembles a slinky(tm) with a triangle cross-section.
By using the angle slider and the -|+ increment buttons you can see what patterns form for any angle from 0 to 180 degrees.
The larger the angle, the bigger the figure drawn so you can shorten the sides with the side length slider to keep the figure in view.
Also, you can swipe|fling the canvas to center the figures.
Try setting the side length to 4 and the angle to 178 to see a polygon that is close to a perfect circle.
Some figures with high angle values may appear slightly irregular - probably due to rounding errors.
The Clock Timer block to draw the polygons is not complicated:

The rest of the procedures and event blocks mainly either initialize variables or make it easier for the user to select a side length or angle.
END