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Homework Help: Trigonal lattice with each angle equal to 120degree

  1. Nov 20, 2006 #1
    1. What happens when the angles between the three sides of a trigonal reach 120degrees?

    I know that at 90degrees, it becomes a simple cubic. At 109degrees, it becomes a body centered cubic. At 60 degrees, it becomes a face centered cubic.
    What about 120degrees? I think that perhaps it should form a structure like a football?

    2. Can pentagons form a lattice? I know that regular pentagons don’t satisfy translational symmetry. But can any pentagon with different side lengths form a lattice?
    I tried making one, but no pentagon satisfies the translation symmetry.



    Many thanks.

    - Farrukh
     
  2. jcsd
  3. Nov 21, 2006 #2

    OlderDan

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    Homework Helper

    For #1 write two vectors in the x-y plane at 120° separation angle. Then write a general vector in 3-D and take the dot procuct with each of the two in-plane vectors and see where it has to point to make the angles to both of those vectors 120°

    For #2, if it did exist you would probably find it here

    http://www.mathpuzzle.com/tilepent.html
     
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