Synonyms: Echinocactus bodenbenderianus (homotypic); Echinocactus stellatus (heterotypic); Gymnocalycium asterium; Gymnocalycium asterium minimum; Gymnocalycium asterium paucispinum; Gymnocalycium asterium var. paucispinum; Gymnocalycium bodenbenderianum (homotypic); Gymnocalycium bodenbenderianum bodenbenderianum; Gymnocalycium obductum; Gymnocalycium occultum (homotypic); Gymnocalycium paucispinum; Gymnocalycium piltziorum; Gymnocalycium platygonum; Gymnocalycium quehlianum var. stellatum (homotypic); Gymnocalycium riojense (homotypic); Gymnocalycium riojense guasayanense; Gymnocalycium riojense kozelskyanum (homotypic); Gymnocalycium riojense paucispinum (homotypic); Gymnocalycium riojense piltziorum (homotypic); Gymnocalycium riojense platygonum (homotypic); Gymnocalycium riojense riojense; Gymnocalycium riojense var. guasayanense; Gymnocalycium riojense var. guthianum; Gymnocalycium riojense var. mirandaense; Gymnocalycium riojense var. pipanacoense; Gymnocalycium riojense var. platygonum (homotypic); Gymnocalycium riojense var. sanjuanense; Gymnocalycium riojense vertongenii; Gymnocalycium stellatum occultum (homotypic); Gymnocalycium stellatum stellatum; Gymnocalycium stellatum var. minimum; Gymnocalycium stellatum var. obductum; Gymnocalycium stellatum var. paucispinum; Gymnocalycium triacanthum