Is it possible to draw a figure that has exactly one reflection symmetry (flip) and one (or more) non-trivial rotational symmetry? (Note: The trivial symmetry is the 0 degrees or 360 degreesrotation).
I am doing this problem for a homework assignment, and was assuming that it wasn't possible, but my proof may not be rigorous enough or even proof at all. This is what i think.
if you assume that something has one reflectional symmetry and one non-trivial rotational symmetry you can rotate it and another reflectional symmetry will become present which contradicts the original assumption of a single reflective symmetry. furthermore any figure with a single reflective symmetry will have atleast 2 rotational non-trivial symmetries.
can someone help me word this so it makes more sense? or steer me on the right path?