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Math Help - symeteries of shapes

  1. #1
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    symeteries of shapes

    how can i go about finding the symetries of these shapes:
    by symmetry i mean both rotational and reflectional:

    square rectangle:

    i get 8 symmetries: reflections in the two diagonals, the horizontal and the vertical, and 4 rotations about 90, 180, 270 and 360 (can be expressed either direction clockwise or counter, i hope you get what i mean)

    also for the square, what are the cycle notations?

    equliateral triangle:

    i can think of only 5?: reflections cutting across from each of the vertices to the bisecter (is this the right term?), and rotations about each vertex by 120 degrees.

    rectangle:

    i get 6, the same as the square minus the diagonal reflecters. because there unsymmetric to them.

    please help me quickly with this and let me know if there is anything i have missed, i want somebody to maybe verify if i have missed anything because i have tried and i cam't think of any others. i have spent 5 hours finding these but i think i have missed some.
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  2. #2
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