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A line segment would have rotational symmetry.
As the name suggests, they are polygons that have one or more lines of symmetry or rotational symmetry of order two or more. A symmetric polygon is not the same as a regular polygon.
If it's a regular 8 sided octagon then it rotational symmetry to the order of 8
If it is a regular 5 sided pentagon then its order of rotational symmetry is 5
Nothing has 1 order of rotational symmetry because in rotational symmetry 1 is none.