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Is Symmetry Limited in Geometry?

  1. Mar 23, 2012 #1
    Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D symmetrical geometric objects/arrangement is limited?

    Is spacial symmetry limited in our 3D world?

  2. jcsd
  3. Mar 23, 2012 #2


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    Hello Islam Hassan and welcome to the forums.

    The question that I have to ask that comes to mind is what the cardinality of the sets themselves involved in the groups you are talking about?

    I don't know that much about group theory (finite or otherwise) but I do know that the sets relating to the associated groups you are referring to are going to have some kind of relation to your answer.
  4. Mar 23, 2012 #3

    I believe that the sets involved may be both finite and infinite; one category of finite simple group in the classification theorem are simple groups of Lie type which, if I recall correctly, can have an infinite number of elements.

  5. Mar 23, 2012 #4
    The answer is known for periodic structures where a "unit cell" is repeated to form an infinite 2D or 3D lattice.

    The application in physics is crystallography.
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