The following solid has an axis of
symmetry about the shown axis. What is the order of rotational
symmetry about the shown axis?
We can recall that an axis of
symmetry is a line in space about which an object may be rotated through 360 degrees
and repeat. In other words, through this
360-degree rotation, the shape will fit on itself more than once. The order of rotational symmetry
tells us how many times that will happen. We can mark one of the lower
vertices in pink. Beginning a rotation of this around
the axis of symmetry, then after 90 degrees of a rotation, this pink vertex would
appear here. After another 90-degree turn, the
pink vertex would be at the top. Another 90 degrees places this pink
vertex here. And completing our 360-degree
rotation would place this pink vertex back where it started.
We can therefore say that this
shape has fitted onto itself or repeated four times, which means that the answer for
the order of rotational symmetry about the shown axis is four.