Synonyms: Cactus compressus (heterotypic); Cactus conopseus; Cactus seitzianus; Mammillaria angularis; Mammillaria bernalensis; Mammillaria brevispina (homotypic); Mammillaria cirrifera (homotypic); Mammillaria compressa longiseta; Mammillaria conopsea; Mammillaria esseriana; Mammillaria scolymoides var. longiseta; Mammillaria seitziana (heterotypic); Mammillaria seitziana var. tolantongensis; Mammillaria senckeana (homotypic); Mammillaria senckei (homotypic); Mammillaria tolimensis; Mammillaria tolimensis brevispina; Mammillaria tolimensis longispina; Mammillaria tolimensis var. brevispina; Mammillaria tolimensis var. longispina; Neomammillaria compressa (homotypic); Neomammillaria seitziana; Neomammillaria subangularis var. longiseta; Neomammillaria tolimensis; Neomammillaria tolimensis var. brevispina; Neomammillaria tolimensis var. longispina