Rotational Symmetry Math Example 1

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Example 1

easy
Determine the order of rotational symmetry and the minimum angle of rotation for a regular hexagon.

Solution

  1. 1
    A regular hexagon has 66 equal sides and 66 equal angles.
  2. 2
    Minimum angle: 360°6=60°\dfrac{360°}{6} = 60°.
  3. 3
    It maps onto itself at rotations of 60°,120°,180°,240°,300°,360°60°, 120°, 180°, 240°, 300°, 360° — that is 66 positions.
  4. 4
    The order of rotational symmetry is 66.

Answer

Order 66; minimum rotation angle 60°60°.
A regular nn-gon has rotational symmetry of order nn, with minimum angle 360°n\frac{360°}{n}. Each additional symmetry position is a multiple of this smallest angle up to 360°360°.

About Rotational Symmetry

A figure has rotational symmetry if it looks identical after being rotated by some angle less than 360°360° about a central point. The order of rotational symmetry is the number of distinct positions where the figure looks the same during a full rotation.

Learn more about Rotational Symmetry →

More Rotational Symmetry Examples

Example 2 medium

Which of the letters 'S' and 'H' has rotational symmetry? State the order and angle for each that qu

Example 3 easy

A figure has rotational symmetry of order [formula]. List all angles of rotation that map it onto it

Example 4 medium

Equilateral triangle [formula] is centred at the origin. A [formula] counterclockwise rotation maps

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