File:Academ One of two hexagons sharing their vertices is regular.svg
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English: In order for some polygon to be regular in Euclidean geometry, it is necessary that all its vertices be evenly spaced on a circle, but this is not sufficient. The image shows two hexagons that share all their vertices, their center, their circumcircle. Each hexagon is symmetric with respect to center T. Hexagon ABDFEC is regular and convex. Its (internal) angle measure equals 120 degrees. However ABCDEF is neither regular nor convex nor simple. The sum of its angles equals 240 degrees: 2 α + 4 β = 2 × 60° + 4 × 30° = 240°. Français : Pour qu’un certain polygone soit régulier en géométrie euclidienne, il est nécessaire que tous ses sommets soient régulièrement espacés sur un cercle, mais ce n’est pas suffisant. L’image montre deux hexagones qui ont en commun tous leurs sommets, leur centre, et leur cercle circonscrit. Chaque hexagone est symétrique par rapport au centre T. L’hexagone ABDFEC est régulier et convexe. Tous ses angles (intérieurs) mesurent 120 degrés. Cependant ABCDEF n’est ni régulier, ni convexe, ni simple. La somme de ses angles est égale à 240 degrés : 2 α + 4 β = 2 × 60° + 4 × 30° = 240°. |
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| Source | Own work |
| Author | Baelde |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:59, 21 June 2012 | | 625 × 500 (2 KB) | Baelde (talk | contribs) | adding an external angle of the regular hexagon denoted by ''α.'' |
| 14:31, 19 June 2012 |  | 625 × 500 (2 KB) | Baelde (talk | contribs) | {{Information |Description ={{en|1=To be a regular polygon in planar geometry, it is not sufficient to be a polygon with all its vertices regularly spaced on a circle. The image shows two hexagons that share their six vertices: ''ABD... |
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