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Math Help - Finding symmetries of a triangular prism

  1. #1
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    Finding symmetries of a triangular prism

    Finding symmetries of a triangular prism-simples.jpg

    The above prism has three identical rectangular faces and equilateral triangles at the top and base. The positions of the faces of the prism have been numbered so that we may represent the elements of the group G of all symmetries of the prism as permutations of the set {1,2,3,4,5}.

    Write down all the symmetries of the prism in cycle form as permutations of the set {1,2,3,4,5} and describe each symmetry geometrically.




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  2. #2
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    Re: Finding symmetries of a triangular prism

    Quote Originally Posted by Jojo55 View Post
    Click image for larger version. 

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    The above prism has three identical rectangular faces and equilateral triangles at the top and base. The positions of the faces of the prism have been numbered so that we may represent the elements of the group G of all symmetries of the prism as permutations of the set {1,2,3,4,5}.

    Write down all the symmetries of the prism in cycle form as permutations of the set {1,2,3,4,5} and describe each symmetry geometrically.




    Here's just one: 2 \rightarrow 3, 3 \rightarrow 5, 5 \rightarrow 2, 1 \rightarrow 1, 4 \rightarrow 4

    i.e. counter-clockwise rotation on z-axis (2 3 5)(1)(4) = (2 3 5)

    Can you find the others?
    Thanks from Jojo55
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    Re: Finding symmetries of a triangular prism

    Quote Originally Posted by majamin View Post
    Here's just one: 2 \rightarrow 3, 3 \rightarrow 5, 5 \rightarrow 2, 1 \rightarrow 1, 4 \rightarrow 4

    i.e. counter-clockwise rotation on z-axis (2 3 5)(1)(4) = (2 3 5)

    Can you find the others?
    Thanks.

    I've got eight with that one included.

    The identity
    1 counter- clockwise rotation on z-axis = (235)
    2 counter- clockwise rotations on z-axis = (253)
    Rotation by pi (where 1 and 4 changes places) = (14)(23)

    Reflections I get
    (25) cuts through the middle of 3, 1 and 4
    (35) cuts through the middle of 2, 1 and 4
    (23) cuts through the middle of 5, 1 and 4
    (14) is a reflection in the horizontal axis
    Last edited by Jojo55; March 25th 2013 at 11:45 AM.
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    Re: Finding symmetries of a triangular prism

    Very naughty this is an Open University T.M.A. assessment question-Don't get caught!
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