Calcium carbonate is one of the most abundant minerals on Earth and a component of natural biogenic materials and man-made cements. The interactions between hydrated calcium carbonate surfaces at nanometer confinement are relevant in dissolution and crystallization processes as well as in adsorption of organic fluids in natural reservoirs. In this work we quantify using atomistic molecular dynamics simulations the water mediated interactions between calcium carbonate surfaces at nanometer separations. We investigate two calcium carbonate polymorphs, calcite and aragonite. We show that the adsorption behavior of water on the (1014) surface of calcite and the (001) surface of aragonite is very different. These differences are reflected in intersurface forces between the two mineral surfaces. The interactions between surfaces feature an oscillatory behavior whose origin is connected to the structuring of water at an intersurface separation <1 nm. We observe adhesion between the surfaces and demonstrate that...