Frailea phaeodisca (Speg.) Backeb. & F.M.Knuth, Kaktus-ABC: 250. 1936 ["1935"] sec. Hunt 2006
- ≡Echinocactus pygmaeus var. phaeodiscus Speg. in Anales Mus. Nac. Buenos Aires, ser. 3, 4: 498. 1905 syn. sec. Hunt 2006
- ≡Frailea pygmaea var. phaeodisca (Speg.) Y.Itô, Cacti, ed. 2: 70. 1952 syn. sec. Hunt 2006
- ≡Astrophytum phaeodiscum (Speg.) Halda & Malina in Acta Mus. Richnov., Sect. Nat., 12(1): 14. 2005 syn. sec. Hunt 2006
- =Frailea perbella Prestlé in Succulenta (Netherlands) 59: 115. 1980 syn. sec. Hunt 2006
- ≡Astrophytum perbellum (Prestlé) Halda & Malina in Acta Mus. Richnov., Sect. Nat., 12(1): 14. 2005 syn. sec. Kew WCVP (2019)