private CubeAction DetermineBelongingCoset(CubeAction e)
                {
                    var eState = new BlockSet(ToStablize);

                    e.Act(eState.State);

                    if (!OrbitToCoset.ContainsKey(eState))
                    {
                        return(null);
                    }

                    var cosetRepresentative = OrbitToCoset[eState];

                    if (Utils.ShouldVerify())
                    {
                        {
                            var cosetReprState = new BlockSet(ToStablize);
                            cosetRepresentative.Act(cosetReprState.State);
                            Utils.DebugAssert(cosetReprState.Equals(eState));
                        }

                        {
                            // States in orbit 1-to-1 maps to each *left* coset (gH). I.e.
                            // iff. e^(-1) * cosetRepresentative stablizes the BlockSet being
                            // observed.  This deduces that, group actions in same *left*
                            // coset, always act the BlockSet being observed to the same state.
                            var reCosetRep = e.Reverse().Mul(cosetRepresentative);
                            Utils.DebugAssert(Stablized.IsStablizedBy(reCosetRep));
                        }

                        {
                            // Iff. e * cosetRepresentative^(-1) stablizes the BlockSet being
                            // observed. This is the condition for *right* coset. It is not what
                            // we need here, and group actions in same *right* coset, may act the
                            // BlockSet being observed to different states.
                            var eRCosetRep = e.Mul(cosetRepresentative.Reverse());
                            // Utils.DebugAssert(observed.IsStablizedBy(eRCosetRep));  // Doesn't hold
                        }
                    }

                    return(cosetRepresentative);
                }