I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem.
Here is the question:
Suppose a cube is oriented before you so that from your point of view there is a top face, a bottom face, a front face, a back face, a left face, and a right face. In the group O of rotational symmetries of the cube, let x rotate the top face counterclockwise 90 degrees, and let y rotate the front face counterclockwise 90 degrees.
(a) Find g in O such that gxg^{-1}=y and g has order 4.
(b) Find h in O such that hxh^{-1}=y and h has order 3.
(c) Find k in O such that kxk^{-1}=x^{-1}.
Thanks in advance.