Rotational Symmetry

Rotational Symmetry

A shape has Rotational Symmetry when it still looks the same after some rotation (of less than one full turn).


Rotational Symmetry
Order 2

Rotational Symmetry
Order 3

How many times it matches as we go once around is called the Order.

Think of propeller blades (like below), it makes it easier.

Examples of Different Rotational Symmetry Order

Order Example Shape Artwork
symmetry order 2 symmetry shape order 2 symmetry art order 2
symmetry order 3 symmetry shape order 3 symmetry art order 3
symmetry order 4 symmetry shape order 4 symmetry art order 4
... and there is also Order 5, 6, 7, and ...
symmetry order 8 symmetry shape order 8 symmetry art order 8
... and Orders 9, 10, and so on.


Try rotational symmetry yourself with Symmetry Artist ... !


symmetry order 1 no

Is there Rotational Symmetry of Order 1 ?

Not really! If a shape only matches itself once as we go around (ie it matches itself after one full rotation) there is really no symmetry at all ...

... because the word "Symmetry" comes from syn- together and metron measure, and there can't be "together" if there is just one thing.


Real World Examples

dart board bronze star london eye
A Dartboard has Rotational Symmetry of Order 10 The US Bronze Star Medal has Order 5 The London Eye has Order ... oops, I lost count!


849, 850, 2137, 2138, 3360, 3361, 3362, 3363, 5033, 5034