Does shape with the following features exist:
It is a regular 2D polygon.
If it is rotated through 50°, it will fit back exactly to its original shape.
BONUS:
If you choose "No", prove why such a shape doesn't exist.
If you choose"Yes", find out the least number of sides that this polygon can have?
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Consider a 360 sided regular polygon. Then rotation by any integer number of degrees will make it fit back to its original shape.