Dodecagon Construction and Tesselation

 

Step 13: The twelve points on the circle define a 12-sided regular polygon, or dodecagon.
Step 14: Draw a circle of radius r=R/2, centered on the first point. Draw lines from the center to the twelve outer points, and mark the intersection of those lines and the inner circle.
Step 15: A second dodecagon is inscribed within the first one.
Step 16: Draw a circle of radius r centered on any inner dodecagon point.
Step 17: Draw another circle of radius r, centered on the next inner dodecagon point.
Step 18: Continue the process until all inner dodecagon points have circles of radius r on them.

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Images © 1999 Aaron Ferrucci except where otherwise noted.