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Math Help - Symmetries question

  1. #1
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    Symmetries question

    Hi there,

    I'm trying to work out the number of symmetries an equilateral triangular prism joined to a tetrahedron at both ends has. I'm seeing 12 symmetries only - can anyone advise me if I am missing out any.

    Thanks!
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  2. #2
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    Re: Symmetries question

    Hello, patrickmustard!

    I'm trying to work out the number of symmetries of an equilateral
    triangular prism with a regular tetrahedron at both ends.
    I'm seeing 12 symmetries only - am I missing out any?

    A symmetry would be a plane which divides the solid into two congruent halves.

    I find only four of them.
    How did you get twelve?

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  3. #3
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    Re: Symmetries question

    Well by symmetries I mean the identity, rotations, reflections and composites, so apologies if I'm misusing the term. I'm seeing 10 of these 'symmetries' - 6 from the tetrahedron (identity, rotation about 120 and 240 degrees, and 3 reflections), and then a reflection through the vertical plane bisecting the prism and then 3 more rotations about the axes through the midpoint of each prism edge and the centre of the opposite face. I hope you understand what I'm talking about, I'm trying to be as clear as I can! Again the shape I'm talking about is a equilateral triangular prism with a tetrahedron attached to each triangle-shaped end of the prism.
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