Describe rotations and reflections that carry rectangles, parallelograms, trapezoids, or regular polygons onto themselves.
Complete all lines of symmetry for a regular polygon
Problem
Count the reflection axes of a regular hexagon through opposite vertex pairs and through opposite side midpoints, and give the total.
Big Picture
What this problem is really about
For an even-sided regular polygon, reflection axes come in two interlaced families. Pair opposite vertices for one family and opposite side midpoints for the other, treating each whole line as one axis rather than counting its two boundary endpoints separately; then combine the two family counts.
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