File:Symmetric group 4; Cayley graph 4,9; dice.svg

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Description (du source XML)
Date 6 September 2007 (original upload date)
Source No machine-readable source provided. Own work assumed (based on copyright claims).
Author No machine-readable author provided. Fool~commonswiki assumed (based on copyright claims).

Graphe de Cayley de S_4 en tant que groupe de rotations d'un dé

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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. Cela 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 correspondront 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 standard sur chaque sommet du graphe.

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Date/TimeThumbnailDimensionsUserComment
current21:27, 4 March 2011Thumbnail for version as of 21:27, 4 March 2011812 × 812 (86 KB)Watchduck (talk | contribs)harmonization with other files
17:51, 16 May 2008Thumbnail for version as of 17:51, 16 May 2008800 × 800 (16 KB)Fool~commonswiki (talk | contribs)
02:24, 6 September 2007Thumbnail for version as of 02:24, 6 September 2007800 × 800 (16 KB)Fool~commonswiki (talk | contribs)''(du source XML)'' === Graphe de Cayley de S_4 en tant que groupe de rotations d'un dé === Le groupe symétrique d'indice quatre et le groupe de rotations d'un cube sont [[:fr:isomorphe|is

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