For 3D rotational symmetry, the ideas are basically the same as 2D Rotational symmetry.

Looking at the picture, when we rotate the cube 360o about the axis, notice that the cube will fit (i.e. match) itself for 4 times.

When this happens, the axis is called the axis of rotational symmetry of order 4.

Note that, the cube has a total of 13 axes of rotational symmetry. You can view them by watching the math video below.

Also, the step-by-step solution shown in the practice question will show you the pictures for these axes.


The illustrations above show the cross sections obtained by cutting a unit cube centered at the origin with various planes. The following table summarizes the metrical properties of these slices.