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clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

dihedral symmetry - rotation / reflection?

1. What are the symmetries of a nonsquare rectangle?
2. What are the symmetries of a parallelogram that is neither a rectangle or a rhombus.
3. What are the symmetries of a rhombus that is not a rectangle?

My thoughts:
1. 4: The identity, 180 degree rotation, vertical reflection and horizontal refletion?
2. 4: The identity, 180 degree rotation, 2 reflections from opposite angles.
3. 4: same as above?

it doesn't seem right because 2 and 3 seems like they shouldn't be the same? THOUGHTS? Thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: dihedral symmetry - rotation / reflection?

1. Correct.
2. No reflections. Only the identity and the 180° rotation.
3. The reflections which don’t work for the parallelogram in 2 work for the rhombus in this case.

Last edited by JaneFairfax (2007-09-03 11:33:59)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: dihedral symmetry - rotation / reflection?

For #2, the reflections from opposite angles results in the same shape but bent left instead of right, so cancel that, just use 180 rotation in the plane.
For #3, the reflections across are okay, since the sides are the same length, it is bent both left and right depending which side is the base.

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