Yes it does whenever you rotate it it will fit in -3 times.
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A regular nonagon with 9 sides has a rotational symmetry of 9.
Rotational symmetry of order 1.
Triangle * * * * * The only triangle with rotational symmetry of order 3 is an equilateral triangle and that has 3 lines of symmetry, not 0. The triskelion (the three legs) on the Isle of Man flag has rotational symmetry of order 3 but no lines of symmetry.
3
A regular triangle (aka equilateral triangle) has three lines of symmetry - these are its medians, In general, a regular n-gon has n lines of symmetry.