Rapicactus in Cactaceae (Berlin) 1942: 24. 1942 sec. Hunt (2006)
- =Lodia in Bradleya 18: 44. 2000 syn. sec. Hunt (2006)
Traditionally included in Turbinicarpus (see there), separated from it by Vázquez-Sánchez & al. (2013) after Turbinicarpus was found to be polyphyletic by them and previously also by Bárcenas & al. (2011). Recent monograph by Lüthy (2003).