# Describe the reflections in an equilateral prism

I can see four reflections of the following prism

(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.

• 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". – Clément Guérin Apr 4 '17 at 19:56
• 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! – ZeroCool Apr 4 '17 at 20:01