A building assembly system that comprises thermoformed high density polyethylene molded components filled with high density polyurethane foam. The molded components are configured in a cube or triangle form and secured against a steel frame to provide a habitable constructed unit. The composition of the high density polyethylene molded components filled with high density polyurethane foam in combination with its connection with a steel frame meets standards for the American Society for Testing and Materials for a habitable structure used by humans. The habitable structure can be used on land or water.