if the atoms are permuted in ways that correspond to flipping the molecule over or rotating it by multiples of 60 degrees. Therefore, replacing any hydrogen by chlorine yields only one chlorobenzene. However, with that replacement, the atom permutations that moved that hydrogen are no longer valid. Only one permutation remains, that corresponds to flipping the molecule over while keeping the chlorine fixed. The five remaining hydrogens then fall into three different equivalence classes: the one opposite to the chlorine is a class by itself (called the para position), the two closest to the chlorine form another class (ortho), and the remaining two are the third class (meta). Thus a second substitution of hydrogen by chlorine can yield three positional isomers: 1,2- or ortho-, 1,3- or meta-, and 1,4- or para-dichlorobenzene. For the same reason, there is only one phenol (hydroxybenzene), but three benzenediols; and one toluene (methylbenzene), but three toluols, and three xylenes. On the other hand, the second replacement (by the same substituent) may preserve or even increase the symmetry of the molecule, and thus may preserve or reduce the number of equivalence classes for the next replacement. Thus, the four remaining hydrogens in meta-dichlorobenzene still fall into three classes, while those of ortho- fall into two, and those of para- are all equivalent again. Still, some of these 3 + 2 + 1 = 6 substitutions end up yielding the same structure, so there are only three structurally distinct trichlorobenzenes: 1,2,3-, 1,2,4-, and 1,3,5-. If the substituents at each step are different, there will usually be more structural isomers. Xylenol, which is benzene with one hydroxyl substituent and two methyl substituents, has a total of 6 isomers: Isomer enumeration and counting Enumerating or counting structural isomers in general is a difficult problem, since one must take into account several bond types (including delocalized ones), cyclic structures, and structures that cannot possibly be realized due to valence or geometric constraints, and non-separable tautomers. For example, there are nine structural isomers with molecular formula C3H6O having different bond connectivities. Seven of them are air-stable at room temperature, and these are given in the table below. Two structural isomers are the enol tautomers of the carbonyl isomers (propionaldehyde and acetone), but these are not stable. See also Coordination isomerism Descriptor (chemistry) Stereoisomer Metamerism (disambiguation) References Isomerism es:Isomería estructural he:איזומרים מרחביים