File:Symmetric group 4; Cayley graph 4,9; octal cubes.svg
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DescriptionSymmetric group 4; Cayley graph 4,9; octal cubes.svg |
Cayley graph of S4 showing all rotations of a cube The colors are the vertices of the RGB color cube and correspond to the numbers 0 to 7 . Red arrows stand for permutation number 9, rotating the cube to the right around the front facing face. Blue arrows stand for permutation number 4, rotating the cube to the left around the topmost and bottommost vertex. |
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current | 01:20, 20 July 2016 | 812 × 812 (254 KB) | Watchduck (talk | contribs) | {{Information |Description ={{en|1=upload forms suck}} |Source ={{own}} |Author ={{Watchduck}} |Date = |Permission = |other_versions = }} |
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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 |