What is the Order of Rotational Symmetry?

Instructor: Emily Hume

Emily is a Reading Specialist and Literacy coach in a public elementary school with a Master's Degree in Elementary Education.

Symmetry can be found in nature, buildings, art, and even in people! In this lesson, you will learn about the order of rotational symmetry: how to determine it and how to recognize rotational symmetry when you see it.

Mirror Image

Look in a mirror! Is the right side of your face the same as the left? If you drew a line down the center of your face, you would see that your face has symmetry, meaning each side of your face matches. If you could fold down that line, the sides of your face would match up.

Round and Round

Look at a picture of a star. If you draw a dot in the center and rotate, or turn, the star on that dot like a pinwheel, you will see that the star's shape doesn't change no matter how many times you turn it. This is called rotational symmetry: No matter how you turn it on that dot, the shape looks the same. For example, a circle has rotational symmetry, but a butterfly (or your face!) does not.

Rotational vs No Rotational Symmetry
Rotational vs No Rotational Symmetry

Shapes aren't the only things that can have rotational symmetry! Pictures and objects that you see every day may also have rotational symmetry. A kickball, the plastic cap on a water bottle, or even a flower could have rotational symmetry.

The Order of Rotational Symmetry

So now that you know what symmetry is and how to recognize rotational symmetry, let's talk about the Order of Rotational Symmetry! If a shape, picture, or object has rotational symmetry, it will also have an order of symmetry, which you can find by counting the number of positions you can turn it and have it still look the same.

For example, look at a square. Picture it rotating, or turning, one time on an imaginary center dot. That counts as Order 1 . Turn it again, and you have Order 2. One more time and you have Order 3. Turn it one last time and you have your square back in its original position, which is also Order 4. So, a square has Rotational Symmetry of Order 4.

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