Is there a rule for determining the ritual purity and impurity of an animal's essence, and is the crocodile essentially impure?

Animals are of two types: pure and impure. The pure type includes animals whose meat is permissible to eat, by scholarly consensus, such as livestock, permissible birds, and fish. As for the impure type, the impurity of dogs, pigs, and whatever is born from them has been explicitly stated. Animals about which there is disagreement include other beasts of prey, domestic donkeys, and mules; some scholars consider them impure, while others consider them pure. The correct view is that mules and donkeys are pure, because the Prophet, peace and blessings be upon him, rode them, and it is impossible to completely avoid them. Among the pure animals are also humans and their remnants (sūr), animals whose meat is permissible to eat and their remnants, and cats and creatures smaller than them in creation, such such as the remnants of a mouse.