A square has 4 lines of symmetry.
A regular hexagon has 6 lines of symmetry.
A regular polygon with 32 sides would have 32 lines of symmetry.
One bisecting each pair of opposite side, that’s 16.
One bisecting each pair of opposite internal angles, that’s 16.
That method works for regular polygons with an even number of sides. But for odd numbers, either:
One bisecting each side.
One bisecting each internal angle.
These are equivalent because each line of symmetry bisects one face and the opposite internal angle.
In any case, for regular polygons, the number of sides equals the number of lines of symmetry.
… I know this seem simplistic, but try if with a 3-gon (equilateral triangle) and you get “3”
and a4-gon (square) you get 4 …
the pattern is too compelling to ignore
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