What is the order of rotational symmetry for a regular hexagon?

The order of rotational symmetry for a regular hexagon is 6.

Rotational symmetry refers to how many times a shape fits onto itself during a full 360-degree rotation. For a regular hexagon, which has six equal sides and angles, this means that it can be rotated in increments of 60 degrees (360 degrees divided by 6) and still look exactly the same as it did before the rotation.

To understand this better, imagine placing a regular hexagon on a piece of paper and marking one of its vertices. If you rotate the hexagon by 60 degrees, the marked vertex will move to the position of the next vertex, and the hexagon will look identical to its original position. This process can be repeated five more times (each time rotating by another 60 degrees), making a total of six positions where the hexagon looks the same. Hence, the order of rotational symmetry is 6.

This concept is important in geometry as it helps in understanding the properties of shapes and their symmetries. Regular polygons, like the hexagon, are often used in problems involving symmetry because their equal sides and angles make them predictable and easier to analyse. Knowing the order of rotational symmetry can also be useful in various applications, such as designing patterns, tiling, and even in understanding molecular structures in chemistry.