Arsinoitherium. Computer illustration and photo-reconstruction of the rhinoceros-like herbivore Arsinoitherium. Arsinoitherium is an extinct genus of paenungulate mammal related to elephants, sirenians, hyraxes and the extinct desmostylians, as well as to other extinct embrithopods. These species were rhinoceros-like herbivores that lived during the late Eocene and the early Oligocene of northern Africa from 36 to 30 million years ago. Arsinoitherium had a face that looked like a rhino's, lived like a hippopotamus but was more closely related to the elephant. Due to the structure of its legs, it was clumsy on land and was better off in the water.