Is there a systematic way to find out what all the symmetries of the following cube are?
Naturally, rotations and reflections along a diagonal or a plane are taken into account.
Of course, by inspection one may be able to find all the symmetries, but what I really mean is;
Given an $n\times n \times n$ cube. If we know that $k$ unit cubes are black and the rest are white.
Is it possible to answer the same question in the general case?
There might be no symmetry at all, but what is the best criterion that can handle the general case?
What is the upper bound of symmetries? and what arrangements of black and white unit cubes give us the upper bound?
P.S. Sorry for asking too many questions in one post.