Finding the order of rotational symmetry about a given axis

geometryrotationssolution-verificationsymmetry

Here is the only example my book gives about rotational symmetry about an axis:
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I am then asked to find the order of rotational symmetry for the following solids:

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I think (a) (b) and (c) all have an infinite order of rotational symmetry and $(d)$ has an order of 8. I want to say that $(b)$ and $(f)$ have order 1 rotational symmetry, because the shape will not look the same until it returns to it's original position. I am correct in my deductions? Thanks in advance

Best Answer

For (a) there are actually infinitely many symmetries, as rotation by any angle is a symmetry, same for (e). For (c) if the base is a square there are 4 symmetries, if it is not a square then just 2 symmetries. The rest of your deductions are correct.

I like the following intuitive picture: See a symmetry as a move that you could do while someone else leaves the room and if they come back they will be unable to detect it.

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