The application of the names Cactus icosagonus Kunth and Cactus humboldtii Kunth is discussed with reference to their historical treatment compared with the various forms of these taxa seen in habitat today. Plants were found in Ecuador which closely match the description of Akersia roseiflora Buining, suggesting that its original type locality in southern Peru was incorrectly stated. The division of Borzicactus icosagonus into three subspecies is proposed and an epitype for one of them is designated.