yes, it in fact does. both!
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Not always. It depends where the line of symmetry is located.
A regular 6 sided hexagon has 6 lines of symmetry
Yes.
A regular hexagon with 6 equal sides will have 3 lines of symmetry
A hexagon need not have any lines of symmetry. Or, it can have just one line of symmetry. A regular hexagon has six lines of symmetry, including three along the lines bisecting the angles and three along the lines formed by bisecting the sides. A regular hexagon has a rotational order of 6.