Plaster of Paris is chemically calcium sulfate hemihydrate (CaSO₄·½H₂O), formed by heating gypsum to remove some water of crystallization. It's called 'hydrated calcium sulphate' because it still contains some water molecules in its crystal structure, unlike anhydrous calcium sulfate. Potassium permanganate and calcium carbonate are entirely different compounds with no relation to Plaster of Paris.