Question 467849: Identify the regular n-gons that have both 12 degree and 20 degree rotational symmetry.
Thank you.
Paul Moore
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! I am not sure if I am interpreting this question correctly, but here is how I would approach it.
A regular n-gon with 30 sides would have a rotational symmetry at 12 degrees, a regualar n-gon with 18 sides would have rotational symetry at 20 degrees.
It seems to me that the smalled n-gon that would have rotatinoal symetry at 12 and 20 degree rotational degree symetry would have to be a divisor of 12, 20 and 360 degrees, the largest would be 4, this would result in 90 faces and vertices on a regular n-gon, the only other two I believe would fit this criteria would be n-gons with 180 faces and 360 faces.
That would be the way I would interpret this question.
Cleomenius.
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