We performed molecular dynamics simulations of diluted solutions of calcium carbonate in water. To this end, we combined and tested previous polarizable models. The carbonate anion forms long-living hydrogen bonds with water and shows an amphiphilic character, in which the water molecules are expelled in a region close to its C-3 symmetry axis. The calcium cation forms a strongly bound ion pair with the carbonate. The first hydration shell around the CaCO3 pair is found to be very similar to the location of the water molecules surrounding CaCO3 in ikaite, the hydrated mineral.