Table of Contents

Last modified on August 3rd, 2023

A shape is said to have a rotational symmetry if after its rotation of anything less than 360°, looks the same. This rotation can be clockwise or anticlockwise.

Geometric shapes like equilateral triangles, squares, pentagons, hexagons, or any other regular polygon posses rotational symmetry. A very common example of rotational symmetry in everyday life is the recycling icon.

If we rotate a square in each step by 90°, the square looks exactly the same. In a full turn 360° there are 4 positions when the square looks exactly the same. Logos of Mitsubishi, Mercedes Benz, or Woolmark also has rotational symmetry.

Some common terms related to rotational symmetry are:

**Center of Rotation**

It is the fixed point around which the object is rotated. For example, paper windmill has its center of rotation around which the treadmill rotates.

Thus a rhombus has a rotational symmetry of order 2.

**Angle of Rotational Symmetry**

The angle of rotational symmetry of an object is the smallest angle at which it can be rotated to coincide with its original shape. For example, a square can be rotated at a minimum of 90° to coincide with itself. Similarly, a hexagon’s angle of rotational symmetry is 60°. We calculate it by simply dividing 360° by the order of the rotational symmetry.

**Order of Rotational Symmetry**

Order (or degree) of rotational symmetry is the number of times a shape can be rotated about its center to keep the look exactly the same as it was before the rotation.

To identify rotational symmetry in any regular shape or object, we should find how many times we can rotate it about its center such that it coincides with its original shape. So, let us check if a 5-star possesses rotational symmetry.

To find, we marked a point on it and then rotated it clockwise a number of times, as shown below.

We found that if we rotate the star 5 times, it returns back to its original form or position. So it shows a rotational symmetry of order 5.

**What is the order of rotational symmetry of a rhombus**?

The diagram shows the order of rotational symmetry when we try rotating a rhombus.

Thus, a rhombus has a rotational symmetry of order 2.

Similarly, alphabets or letters like H, I, N, S, and Z also possess rotational symmetry.

The table shows the order and angle of rotational symmetry for some common geometric shapes.

Shape | Order of rotational symmetry | Angle of rotational symmetry |
---|---|---|

Rectangle | 2 | 180° |

Equilateral triangle | 3 | 120° |

Square | 4 | 90° |

Pentagon | 5 | 72° |

Hexagon | 6 | 60° |

Heptagon | 7 | 51.43° |

Octagon | 8 | 45° |

Nonagon | 9 | 40° |

Decagon | 10 | 36° |

Last modified on August 3rd, 2023