Dodecagon Construction and Tesselation

 

Step 19: Choose an inner circle and mark all intersections of that circle and any other.
Step 20: Continue the process, marking all intersections of inner circles with each other.
Step 21: Walk around an inner circle, drawing straight line segments between each pair of adjacent points marked on the circle. Another dodecagon is created.
Step 22: Mark another circle in the same way, creating another dodecagon.
Step 23: Finish off all the inner circles, creating a total of 12 small dodecagons inside the large one. The large dodecagon is tesselated with three different rhombuses, one a square. All rhombuses have sides of length R sin 15°.

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Images © 1999 Aaron Ferrucci except where otherwise noted.