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Group symmetry

  1. Dec 5, 2008 #1
    How many symmetries (and what symmetries) and how many elements do the transformation groups of the equilateral triangle and the icosahedron have?

  2. jcsd
  3. Dec 5, 2008 #2


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    |D3| and |A5 x Z2|, respectively.

    How about you start by writing down those of the equilateral triangle. There aren't that many so you can easily list them.
  4. Dec 5, 2008 #3
    3 reflections and 3 rotations, right? But what does |D3| mean?
    And what is |A5 x Z2|?

    Where can I look up the symmetries for other geometric objects, like for example the other platonic solids?

    And what about the number of elements, how do i find out about those?
  5. Dec 5, 2008 #4
    If you've studied groups much, you should recognize what each of those groups are. D3 is the dihedral group of order 6, A5 × Z2 is the direct product of A5, the alternating group of degree 5, which has 5!/2 = 60 elements, and Z2, the cyclic group of order 2.

    Thus, the equilateral triangle has 6 symmetries, and the icosahedron has 120.
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