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Stupid/ simple question about g2

  1. Nov 14, 2007 #1
    I really don't know that much representation theory or group theory.

    I was looking at Garrett lisi's presentation, and I was looking at the 3d root system of g2. It struck me that it looked similar to a dodecahedron inscribed in a cube. Now, I do know that the dodecahedron group, and the cube group are dual. Can g2 be broken up into the symmetries of a cube, and a dodecahedron?
  2. jcsd
  3. Nov 15, 2007 #2
    I meant dual Octahedron is dual to the cube. sorry
  4. Nov 23, 2007 #3

    Chris Hillman

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    The Root System G_2

    Unless I misunderstand what you are talking about, I think you mean 2d; see James E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, 1972, Fig. 1 on p. 44, for a picture of the root system [itex]G_2[/itex].
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