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I can see four reflections of the following prism

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(1 4), (3 5), (2 5) and (2 3), which are reflections in the planes passing through the centre of each of the faces 2, 3, 5 and their perspective opposite vertical edges.

What are the two other reflections? I found (2 3 5)(1 4) and (2 5 3)(1 4) but can't imagine them geometrically.

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    $\begingroup$ They are not reflexion. A reflexion is supposed to be of order $2$ whereas the elements you are looking for are of order $6$. English is not my native language but according to wikipedia it is called "improper rotation" : en.wikipedia.org/wiki/Improper_rotation. I think they are hard to see "geometrically". $\endgroup$ – Clément Guérin Apr 4 '17 at 19:56
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    $\begingroup$ I presumed they were reflections as I obtained them by composing a rotation with reflection which results in a reflection. My book doesn't say anything about these improper rotations. Very interesting! Many Thanks Clément! $\endgroup$ – ZeroCool Apr 4 '17 at 20:01

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