Synonyms: Cactus cornifer (homotypic); Cactus pfeifferianus; Cactus radians; Cactus radians var. pectinoides; Cactus scolymodes; Cactus scolymoides; Coryphantha bernalensis; Coryphantha cornifera; Coryphantha cornifera var. scolymoides; Coryphantha cornuta; Coryphantha daemonoceras; Coryphantha daimonoceras; Coryphantha impexicoma (homotypic); Coryphantha maliterrarum; Coryphantha radians var. impexicoma; Coryphantha radians var. pectinoides; Coryphantha schwarziana; Coryphantha scolymoides; Echinocactus cornifer (homotypic); Echinocactus cornifer var. impexicomus; Echinocactus cornifer var. longisetus; Echinocactus cornifer var. muticus; Echinocactus cornifer var. nigricans; Echinocactus cornifer var. scolymoides; Echinocactus corniferus; Echinocactus corniferus var. impexicomus; Echinocactus corniferus var. longisetus; Echinocactus corniferus var. muticus; Echinocactus corniferus var. nigricans; Echinocactus corniferus var. scolymoides; Echinocactus radicans; Mammillaria cornifera (homotypic); Mammillaria cornifera f. scolymoides; Mammillaria cornifera var. impexicoma; Mammillaria cornifera var. implexicoma; Mammillaria cornuta (homotypic); Mammillaria daemonoceras (homotypic); Mammillaria daimonoceras; Mammillaria impexicoma; Mammillaria pfeifferiana; Mammillaria radians; Mammillaria radians f. scolymoides; Mammillaria radians var. daimonoceras; Mammillaria radians var. globosa; Mammillaria radians var. impexicoma (homotypic); Mammillaria radians var. scolymoides; Mammillaria scolymoides; Mammillaria scolymoides var. nigricans; Mammillaria scolymoides var. raphidacantha