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Symmetries of a Tetrahedron video

  1. May 7, 2013 #1

    I made this video with my iphone depicting the Symmetries of a Tetrahedron for a presentation I did recently:

    I have been searching and trying to figure out if I have presented it correctly that a Tetrahedron has full S4 symmetry if we could reflect it in a "higher dimension."

    I was basing this statement off of the fact that the rotational symmetry equilateral triangle is achieved through even permutations. However, the odd permutation suggest a reflection that requires the triangle to move through an additional dimension of space.

    I am assuming we can say the same about a Tetrahedron where odd permutations can only be applied if we could move the shape through a higher spacial dimension. Is this stated correctly?

    Thank you,

    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. May 7, 2013 #2

    Ben Niehoff

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    The rotational symmetry group of a regular tetrahedron in 3-space is ##A_4##, the even permutations of 4 elements. If reflections are allowed, then you have ##S_4##, the full group of permutations.
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