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Geometry Toolkit

Geometry

Counting the order

  • The order of rotational symmetry counts how many times a shape looks unchanged during one full turn about its centre
  • Returning to the starting position always counts, so the smallest possible order is 1
  • A shape of order 1 is normally described as having no rotational symmetry
  • With tracing paper, draw an arrow to mark the starting position so you can tell when a full turn is complete
    • A parallelogram has order 2 with no lines of symmetry, which shows the two kinds of symmetry are independent
    • A regular polygon with n sides has order n and n lines of symmetry
A triangular prism drawn four times as it turns about an axis running along its length, coming back to a matching position three times in a full turn, so its rotational symmetry about that axis is order 3
Source: Planes of symmetry by Save My Exams