File:Symmetric group 4; Cayley graph 4,9; matrices.svg
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DescriptionSymmetric group 4; Cayley graph 4,9; matrices.svg | Cayley graph of S4 | |||
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This vector image was created with Inkscape by v . |
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I, the copyright holder of this work, hereby publish it under the following license:
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 03:11, 14 October 2014 | 812 × 812 (230 KB) | Wereldburger758 (talk | contribs) | Valid SVG now. | |
00:50, 5 March 2011 | 812 × 812 (316 KB) | Watchduck (talk | contribs) | {{Information |Description=Cayley graph of S<sub>4</sub> |Source=*GrapheCayley-S4-Plan.svg |Date=2011 |Author=*GrapheCayley-S4-Plan.svg: [[Us |
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Short title | Graphe de Cayley de S_4 en tant que groupe de rotations d'un dé |
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Image title | Le groupe symétrique d'indice quatre et le groupe de rotations d'un cube sont isomorphes.
Ici on a choisi deux rotations génératrices: 90 degrés autour d'une face, et 120 degrés autour d'un sommet. Celà correspond à la présentation < a,b | a^4 = b^3 = (ab)^2 = 1 > On peut dessiner le graphe de Cayley de cette présentation sur une surface de genre 0, qui sera divisée en 26 régions, et coloriée avec 3 couleurs. D'ailleurs les régions de la surface corresponderont aux sommets, arêtes, et faces d'un cube, et on pourra choisir une seule couleur pour tous les sommets, une pour les arêtes, et une pour les faces. Pour mieux illustrer l'action du groupe, on a aussi dessiné une position d'un dé standardsur chaque sommet du graphe. |
Width | 812.125 |
Height | 812.09375 |