Describe rotations and reflections that carry rectangles, parallelograms, trapezoids, or regular polygons onto themselves.
List all symmetries of a regular polygon
Problem
List every symmetry of a regular hexagon, counting the identity as the \(0°\) rotation. Give the rotations, reflection-axis types and counts, and total number of symmetries.
A complete symmetry inventory has two families that should be counted separately before they are combined. Generate rotations from the equal central-angle step, including the identity, and generate reflections of this even-sided regular polygon through opposite vertex pairs and opposite side-midpoint pairs.
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