Editing Structural isomer (section)

===Structural symmetry and equivalent atoms===
Structural symmetry of a molecule can be defined mathematically as a [[permutation]] of the atoms that exchanges at least two atoms but does not change the molecule's structure. Two atoms then can be said to be structurally [[equivalence relation|equivalent]] if there is a structural symmetry that takes one to the other.<ref name=faul2010/>

Thus, for example, all four hydrogen atoms of [[methane]] are structurally equivalent, because any permutation of them will preserve all the bonds of the molecule.

Likewise, all six hydrogens of [[ethane]] ({{chem|C|2|H|6}}) are structurally equivalent to each other, as are the two carbons; because any hydrogen can be switched with any other, either by a permutation that swaps just those two atoms, or by a permutation that swaps the two carbons and each hydrogen in one methyl group with a different hydrogen on the other methyl. Either operation preserves the structure of the molecule. That is the case also for the hydrogen atoms in [[cyclopentane]], [[allene]], [[2-butyne]], [[hexamethylenetetramine]], [[prismane]], [[cubane]], [[dodecahedrane]], etc.

On the other hand, the hydrogen atoms of [[propane]] are not all structurally equivalent. The six hydrogens attached to the first and third carbons are equivalent, as in ethane, and the two attached to the middle carbon are equivalent to each other; but there is no equivalence between these two [[equivalence class]]es.