Here, A ⃗ ⃗ is understood to be the origin and SO(3) denotes the space of rotations about A ⃗ ⃗ (that is, the rotational external degrees of freedom). Note that 𝒞 𝑛 assumes that no two B-atoms are in the same position. Our general approach will allow this to happen which, in mathematical terms, will lead to a compactification of 𝒞 𝑛 .