Question 467849
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.