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There is a point inside a polygon such that if you rotate the polygon around that point clockwise by 55 degrees, the polygon coincides with itself. What is the minimum number of vertices that this polygon can have?

 
Guest Sep 15, 2018
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There is a point inside a polygon such that if you rotate the polygon around that point clockwise by 55 degrees, the polygon coincides with itself. What is the minimum number of vertices that this polygon can have?

 

I'm going to guess a bit.

I think the polygon probably has to be regular (all sides and angles the same)  And the rotation point is in the middle. 

 

360/55 =72/11 = 6.5454545454545455 sides but it has to have a whole number of sides so this is no good

72/11*11 = 72

Well if it has 72 sides this will work.

 

360/72 = 5  So every 5 degrees it will rotate onto itself.   So it will overlap itself 11 times in a rotation of 55 degrees.

 

Anyway, my guess is 72 sides. Can someone do it with less sides?

 
Melody  Sep 16, 2018

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