Synonyms: Cactus crocidatus; Cactus polythele (homotypic); Cactus tetracanthus; Mammillaria columnaris; Mammillaria crocidata; Mammillaria durispina; Mammillaria hidalgensis; Mammillaria hoffmanniana; Mammillaria kelleriana; Mammillaria kewensis; Mammillaria loricata (homotypic); Mammillaria neophaeacantha; Mammillaria polythele durispina; Mammillaria polythele var. columnaris; Mammillaria spectabilis (homotypic); Mammillaria subdurispina; Mammillaria tetracantha; Mammillaria xochipilli; Neomammillaria crocidata; Neomammillaria durispina; Neomammillaria hidalgensis; Neomammillaria hoffmanniana; Neomammillaria kewensis; Neomammillaria polythele (homotypic); Neomammillaria subdurispina