So i began reading up on some group theory and I came across an interesting question, what is the order of the group of symmetries on of a n-sided regular polygon?(adsbygoogle = window.adsbygoogle || []).push({});

with a square it's 8, triangle it's 4.

I feel like i'm missing something with the pentagon cuz i'm only finding these:

the 5 rotations, two diagonal reflections which are NOT the same as that for the square, reflection over the vertical axis.

i'd appreciate any casual discussion on the topic as I find it fascinating,

at the very beginning because symmetries behave very much like permutations (if we label vertices) I thought there might be a relationship between this set and the symmetric group of {1,...n}? But there are obviously permutations that no movement of a polygon in the plane can mimic.

true or false: the group of symmetries of a n-sided regular polygon in the plane is isomorphic to a subset of the symmetric group of {1,...,n}.

cheerio!

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# Group of symmetries on a regular polygon

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