Finding All Symmetries of a Regular Hexagon

Pre-Algebra · Axiom Academy

EXAMPLE Finding All Symmetries of a Regular Hexagon Counting the lines of symmetry and the rotational symmetry of a regular hexagon. A regular hexagon is a six-sided polygon with all sides equal and all angles equal. Find every symmetry it has: how many lines of symmetry , and what its rotational symmetry is. All six lines of symmetry pass through the center. Work through the steps below to count them yourself. Nice work — you've found every symmetry of a regular hexagon. 6 lines of symmetry: 3 through pairs of opposite vertices, plus 3 through pairs of opposite edge midpoints. Rotational symmetry of order 6: the hexagon looks identical after rotating by and about its center — each turn is . A pattern for regular polygons: a regular n -gon has n lines of symmetry and rotational symmetry of order n . A square ( n=4 ) has 4 of each; the hexagon ( n=6 ) has 6. That high degree of symmetry is exactly why hexagons tile the plane so neatly — think of honeycombs and floor tiles.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.