Mammillaria polyedra Mart. in Nova Acta Acad. Caes. Leop.-Carol. German. Nat. Cur. 16: 326. 1832 sec. Hunt 2016
- =Mammillaria multiseta C. Ehrenb. in Allg. Gartenzeitung 17: 242. 1849 syn. sec. Guzmán & al. 2003
- =Cactus polyedrus (Mart.) Kuntze, Rev. Gen. Pl. 1: 261. 1891 syn. sec. Guzmán & al. 2003
- =Neomammillaria polyedra (Mart.) Britton & Rose, Cactaceae (Britton & Rose) 4: 102. 1923 syn. sec. Guzmán & al. 2003