you are all right. The book I have ("The Cactus Family") doesn't even have notocactus. I'm not sure what is the correct nomenclature.
Parodia Ottonis (Lehmann) N. P. Taylor 1987 Cactus ottonis Lehmann 1827, Echinocactus ottonis (Lehmann) Link & Otto 1830, Malacocarpus ottonis (Lehmann) Britton & Rose 1922, Notocactus ottonis (Lehmann) A. Berger 1929 Echinocactus tenuispinus Link & Otto 1827, Notocactus tenuispinus (Link & Otto) Herter 1955 Echinocactus arechavaletae Spegazzini 1905, Malacocarpus arechavaletae (Spegazzini) A. Berger 1929, Notocactus arechavale- tae (Spegazzini) Herter 1943 Echinocactus ottonis var. uruguayus Arechavaleta 1905, Notocactus uruguayus (Arechavaleta) Herter 1943 Parodia paraguayensis Spegazzini 1923 Notocactus acutus F. Ritter 1979 Notocactus arechavaletae var. horstii F. Ritter 1979, Parodia ottonis subsp. horstii (F. Ritter) Hofacker 1998 Notocactus grandiensis S. Bergner 1989, notvalidly published ?Notocactus ruoffii N. Gerloff 1993 Plants solitary at first, later forming clumps. Stems globose, often tapering toward bases, light or dark green or blue-green, 3-15 cm (1.2-5.9 in) in diameter, with white wool apically. Ribs 6-16, well defined, rounded or acute. Areoles usually few. Spines hairlike, straight, curved or twisted. Central spines 1-4, brownish, reddish brown or yellowish, 8-40 mm (0.3-1.6 in) long. Radial spines 4-15, whitish to yellowish to brownish, 5-30 mm (0.2-1.2 in) long. Flowers usually yellow, rarely orange-red, 5-6 cm (2-2 A in) long; floral tubes with brownish wool and bristles. Fruits ovoid to short cylindrical, thick walled, dehiscent, 0.9-1.2 cm (0.4-0.5 in) in diameter, often with large numbers of seeds. Seeds bell shaped, glossyblack, strongly tuberculate. Distribution: northeastern Ar- gentina, southern Paraguay, Uruguay, and southern Brazil. Parodia ottonis is a widespread and variable species, ac- counting for the many names it has received. Two subspecies are recognized. Subspecies ottonis has stems rarely exceed- ing 6 cm (2.4 in) in diameter, only 10 ribs, and 3-4 central spines; it occurs widely in southern Brazil, Uruguay, and Ar- gentina. Subspecies horstii has stems often to 15 cm (5.9 in) in diameter, 12-16 ribs, and 1-4 central spines; it occurs in Rio Grande do Sul, Brazil.
Here is some reading on PARODIA
Parodia Parodia comprises cacti that are small, mostly globose, freely producing colorful flowers. Parodia is popular among hob- byists and consequently has been subdivided into hundreds of species, many of which clearly are not justified. Anatomi- cal and morphological studies by Reto Nyffeler and other European botanists have helped in our understanding of Pa- rodia and related genera. Nigel Taylor (1989b) and Urs Eggli and Nyffeler (1998) have concluded that Parodia has been badly oversplit into numerous genera that cannot be sus- tained. Eggli and Nyffeler believe that the segregates repre- sent different lineages derived from the core of Parodia in the strict sense. Thus the cacti are closely related with the dif- ferent seed types that characterize the segregates simply rep- resenting adaptations to dispersal by different means. They suggest that Parodia should be broadly interpreted to include Brasilicactus, Brasiliparodia, Eriocactus, Notocactus, and Wig- ginsia. Unfortunately, these scientific conclusions have upset many hobbyists, who have argued passionately for contin- ued recognition of related groups, particularly Notocactus, as distinct genera. On the other hand, they also believe that Parodia should perhaps include Blossfeldia and Frailea. There is a nomenclatural problem regarding Frailea, how- ever. If Parodia were to include Frailea, then Parodia would have to be conserved over the older name Frailea, as pro- posed by Eggli and Nyffeler. For the time being, the International Cactaceae Systemat- ics Group has elected to recognize the broadly defined Paro- dia with 66 species but maintain Blossfeldia and Frailea as separate. Specialists believe that several of the species should be subdivided into subspecies, but since few such nomen- clatural combinations have been made, only a few are in- cluded in the treatment here. Publications by Tony Mace (1980) and Walter Weskamp (1992) have summarized the hobbyists' approach to Notocactus and Parodia, respectively. Additional valuable contributions have also been made by Roberto Kiesling and Omar Ferrari (1990), Kiesling (1995), John Brickwood (1997a,b), Nyffeler (1997a), Andreas Ho- facker (1998), and Hofacker and Pierre Braun (1998). None- theless, the huge number of names has created a taxonomic nightmare that will be difficult to straighten out. Parodia (type, Echinocactus microspermus = P. micros- perma) was described in 1923 by Carlos Spegazzini to replace the illegitimate name Hickenia, used by Nathaniel Britton and Joseph Rose in 1922. The name Parodia honors Do- mingo Parodi, an early student of the flora of Paraguay. Pa- rodia is low growing, either solitary or clustering, globose to cylindrical, with ribs or tubercles. Flowers are borne subapi- cally and are open during the day; they tend to be funnel- form or bell shaped, brightly colored, and bristles and hairs are often present on the floral tubes and pericarpels. The seeds are diverse, a feature that has led many to argue for the recognition of several genera. Some possess a strophiole or caruncle, terms often used synonymously though their de- velopment is different (Buxbaum 1950,202). The latter term probably is most appropriate for Parodia. Parodia Spegazzini 1923 Malacocarpus Salm-Dyck 1850, illegitimate name, not F. E. L Fischer & C. A. Meyer 1843 (Rutaceae) Echinocactus subg. Notocactus K. Schumann 1898, Notocactus (K. Schumann) Fric 1928 Brasilicactus Backeberg 1942 Eriocactus Backeberg 1942 Wigginsia D. M. Porter 1964 Brasiliparodia F. Ritter 1979 Subfamily Cactoideae, tribe Notocacteae. Plants solitary or clus- tering, low growing. Stems fairly small, globose to short cylindrical. Ribs present, somewhat tuberculate or completely forming tubercles. Areoles usually densely woolly when young. Spines few to many, vari- able. Flowers borne subapically, open during the day, funnelform to bell shaped, brightly colored; floral tubes and pericarpels often with hairs and bristles, the latter sometimes restricted to the upper parts of the tubes. Fruits globose to club shaped to cylindrical, dry or nearly so, woolly or bristly; thin walled and disintegrating basally or nearly so, or thick walled and dehiscing laterally, or fleshy and pink. Seeds diverse in shape, reddish brown to black, small, with large hilum, some with caruncles, some with spiny or hairlike projections. Distribution: oc- curring widely throughout eastern South America, mostly east of the Andes in Bolivia, Brazil, Paraguay, Uruguay, and Argentina.
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