1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Group theory: point group of a cube

  1. Feb 29, 2004 #1
    what is the point group of a cube?
     
  2. jcsd
  3. Mar 1, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    it is the same as the ordinary symmetry group. (rotations and reflections). if the question was what's this group, then it is a group of order 48, you can get a presentation of it by labelling the vertices. It is abstractly isomorphic to S_4 x C_2, symmetric group on 4 letters direct product cyclic group of order 2.

    To see the iso with S_4xC_2 imagine drawing in the diagonals of the box, there are 4 of them. the symmetries permute these 4 objects, the C_2 part is because there are reflections too.
     
    Last edited: Mar 1, 2004
  4. Mar 1, 2004 #3

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    If I remember my solid state course correctly, the group for a cube is [tex]O_{h} [/tex]. This takes into account the inversion symmetry. I believe it is written as [tex]O_{h} = S_{4} x C_{2} [/tex].

    dt
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Group theory: point group of a cube
  1. Group theory (Replies: 3)

  2. Group Theory (Replies: 6)

  3. Group theory (Replies: 1)

Loading...