The author discusses in this paper relations like the use of geometric structures (chain structures, graphs) to represent loops. With derivations like loop derivation, permutation derivation of a loop \((P,+)\) the author translates properties of one structure into properties of the other. Of particular interest to the author are invariant reflection structures \((P,\;)\) and their corresponding K-loops. The author discusses also: symmetric chain structures, immersions of permutation sets in chain structures, loops derived from point reflection spaces, loops with fibrations.