Finding symmetries both geometrically and analytically. PLEASE HELP

  1. Finding symmetries both geometrically and analytically. PLEASE HELP!!!

    I have found this question and not sure where to begin in terms of solving it. PLEASE HELP!!

    Consider a double square pyramid . Introduce a coordinate P system so that the
    vertices of P are:

    A=(2,0,0)
    B=(0,2,0)
    C=(-2,0,0)
    D=(0,-2,0)
    E=(0,0,1)
    F=(0,0,-1)

    List the symmetries of P. Do this both geometrically and analytically.
     
  2. jcsd
  3. micromass

    micromass 19,224
    Staff Emeritus
    Science Advisor
    Education Advisor

    Re: Finding symmetries both geometrically and analytically. PLEASE HELP!!!

    You can start by sketching the figure. Now, what symmetries can you see in the figure?
     
  4. Re: Finding symmetries both geometrically and analytically. PLEASE HELP!!!

    I tried drawing it out, but I just have a lot of trouble with 3D shapes. I have trouble drawing figures with 3 coordinates (x,y,z).
     
  5. Re: Finding symmetries both geometrically and analytically. PLEASE HELP!!!

    I would assume there would some kind of rotation with cycle 3, being that it is a pyramid.
     
  6. Deveno

    Deveno 906
    Science Advisor

    Re: Finding symmetries both geometrically and analytically. PLEASE HELP!!!

    normally, there would be. but the vertices at E and F being at (0,0,1) and (0,0,-1) preclude those symmetries.
     
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