I am from a chemistry background and I haven't taken abstract algebra, so it is possible that this question may be basic. This is the problem that I have:
Suppose that I have an object A, which is a tetrahedron inside a cube. By applying all symmetry operations on A, I can determine the space group of the object.
This seems rather cumbersome. One has to worry about the position of each object as well as the dimension (i.e. whether it is a triangle, square, hypercube, etc). For example:
Has a different symmetry than:
I was wondering whether there were some relations that I could take advantage of to simplify the problem.
Is there a theorem that says something along the lines of:
If an object has symmetry x and is inside an object of symmetry y, the highest symmetry attainable is z?