When looking at a cube you see either two surfaces across an edge or three surfaces around an apex. Is it possible to arrange a non-symmetrical character (e.g."R") at 0,90,180 or 270 degrees rotation on each surface of a cube such that no two characters viewed across an edge appear the same way up and no three characters viewed from an apex appear as if they rotate around the apex (e.g. had all the top left corners of the character's square touching at the apex) ?
It is possibly obvious that I am not a mathematician which means two things :
1 responses need to be couched in "layman's" terms
2 my efforts so far have been experimental rather than mathematical:
So far I can produce arrangements that fulfil the first (edge) criteria but can't get rid of one set of characters that rotate around an apex. When I destroy a rotation at one apex it pops up around another apex ......
I'd like a mathematician to tell me my target either can or can't be achieved so I know whether to keep trying or not. Regards Ken