Thread: 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.

Take a look here. It doesn't look to me like you missed anything.