There are 30026 symmetry-distinct ways to arrange 20 water molecules in a dodecahedral cage with nearly optimum hydrogen bond lengths and angles, analogous to the arrangements that give rise to the zero-point entropy in ice-Ih. The energy of hydrogen bond isomers in (H2O)(20), assumed to be similar in the past, differs by up to 70 kcal/mol. The isomers differ widely in their hydrogen bond lengths, some exhibiting bond lengths as short as similar to2.4 Angstrom. The differences among the isomers extends to their chemical properties: In some arrangements one or more water molecules spontaneously self-dissociate, giving rise to spatially separated excess proton and hydroxyl ion units in the cluster. Isomers that exhibit these unusual properties can be identified by features of their hydrogen bond topology. (C) 2003 American Institute of Physics.