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If you're talking about convex polygons with equal sides (eg. equilateral triangles, squares, pentagons, hexagons, etc.), then the relationship is a very direct one. In those cases, there are as many lines of symmetry as there are points in the polygons. A triangle has three lines of symmetry, a square has four, a pentagon five, etc.

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Q: What is the linear relationship between number of sides and number of lines of symmetry?
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