- #1
SiddharthM
- 176
- 0
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?
with a square it's 8, triangle it's 4.
I feel like I'm missing something with the pentagon because 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!
with a square it's 8, triangle it's 4.
I feel like I'm missing something with the pentagon because 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!