Dodecagon Construction and Tesselation

Step 1: Choose any point in the plane. | |

Step 2: Draw a circle (conceptually, at least) of radius R. Mark any point on that circle. | |

Step 3: Draw another circle of radius R, centered on the second point. Mark the two intersections of the two circles. | |

Step 4: Draw circles of radius R around the two new points, and mark the intersections of the circles. | |

Step 5: Draw another pair of circles around the two newest points, and mark their intersection with each other and with the first circle. | |

Step 6: The 6 points just marked inscribe a hexagon of side length R, centered on the first point. |

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Images © 1999 Aaron Ferrucci except where otherwise noted.