Antarctic coastal sea ice often grows in water that has been supercooled by interaction with an ice shelf. In these situations, ice crystals can form at depth, rise and deposit under the sea-ice cover to form a porous layer that eventually consolidates near the base of the existing sea ice. The least consolidated portion is called the sub-ice platelet layer. Congelation growth eventually causes the sub-ice platelet layer to become frozen into the sea-ice cover as incorporated platelet ice. In this study, we simulate these processes in three dimensions using Voronoi dynamics to govern crystal growth kinetics. Platelet deposition, in situ growth and incorporation into the sea-ice cover are integrated into the model. Heat and mass transfer are controlled by diffusion. We extract and compare spatial-temporal distributions of porosity, salinity, temperature and crystallographic c-axes with observations from McMurdo Sound, Antarctica. The model captures the crystallographic structure of incorporated platelet ice as well as the topology of the sub-ice platelet layer. The solid fraction, which has previously been poorly constrained, is simulated to be ∼0.22, in good agreement with an earlier estimate of 0.25 ± 0.06. This property of the sub-ice platelet layer is important for biological processes, and for the freeboard-thickness relationship around Antarctica.