## Rotational Symmetry

A figure has

__rotational symmetry__if the object can be rotated about a fixed point without changing the overall shape.

e.g. Consider the following equilateral triangle, if you rotate by 120°, you get the same figure.

Order of Rotational Symmetry

The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°.

Thus an equilateral triangle as 3-fold rotational symmetry or its order of rational symmetry is 3. An isosceles triangle has an order of rotational symmetry of 1. While for scalene triangle (three sides are unequal), its order of rotational symmetry is 1.

All figures have an order of rotational symmetry of at least 1.

*Guess what is the order symmetry of a circle?*

Here is a table that lists Lines/Axes Symmetry and Order of rotational symmetry of common geometric shapes.

Shape | Lines/Axes of symmetry | Order of rotational symmetry |
---|---|---|

Equilateral triangle | 3 | 3 |

Isosceles triangle | 1 | 1 |

Scalene triangle | 0 | 1 |

Parallelogram | 0 | 2 |

Square | 4 | 4 |

Rectangle | 2 | 2 |

Rhombus | 2 | 2 |

Trapezium | 0 | 1 |

Isosceles trapezium | 1 | 1 |

Kite | 1 | 1 |

Regular pentagon | 5 | 5 |

Regular hexagon | 6 | 6 |

Regular octagon | 8 | 8 |

Circle | ∞(infinite) | ∞ |

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