File:Abyss of dodecagons with alternate colours.svg
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English: A regular dodecagon is either convex or stellated. Given such a convex polygon, we can draw twelve equal diagonals without lifting the pencil, provided that any diagonal subtends an arc that measures 5 × 360° / 12 = 5 × 30° = 150°, on the circumcircle of the dodecagon. These diagonals are the sides of a stellated dodecagon, which has the same vertices as the initial convex dodecagon. Each of these twelve segments contains a side of a concentric dodecagon, which is a reduction of the initial convex dodecagon to scale tan 15° = 2 - √3. We can consider this new convex dodecagon as a given dodecagon, in order to repeat the process: we construct two other dodecagons, one stellated and the other convex, and two others again, more and more small, indefinitely. We call this an infinite iteration of the geometric construction. |
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| Source | Own work |
| Author | Baelde |
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| current | 09:40, 2 July 2012 | | 750 × 750 (943 bytes) | Baelde (talk | contribs) | {{Information |Description ={{en|1=A regular dodecagon is either convex or stellated. Given such a convex polygon, we can draw twelve equal diagonals without lifting the pencil, provided that any diagonal subtends an arc that measures {... |
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