Video: Identifying Symmetry in Three-Dimensional Figures

The following solid has an axis of symmetry about the shown axis. What is the order of rotational symmetry about the shown axis?

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Video Transcript

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.

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