Rotating coins about triangles

Suppose we have the following arrangement of five coins:



We are allowed to perform one of two operations ($L$ or $R$) in each turn. We can either rotate the three coins around the left triangle $120^{\circ}$ clockwise or the three coins around the right triangle $120^{\circ}$ clockwise on any turn. For example, this is what the diagram would look like after a $L$ move:



Then the following is what the diagram would look like after a $R$ move from the above position (thus a $LR$ move from the original position where the string of $L$ or $R$ denotes the order of the moves from the original position):



Is it ever possible to attain the following two positions from the original position with a series of these $L$ or $R$ moves? If not, why?

(a)

(b)

L and R are

(13)(34) and (24)(45), both even permutations.

a) and b) are

(12)(14) and (12), which are even and odd permutations, respectively.

Therefore

a) is reachable (e.g. via RRLRLL) and b) is not.

operations are both

even permutations

so

(a) can and (b) cannot both be attained as coins 2 and 4 end up swapped

which one of both can

I need to figure out but I guess is less important, because any even or odd can