Thelocactus rinconensis ssp. rinconensis (Poselger) Britton & Rose, Cact. 4: 7 (1923).

Basionym: Echinocactus rinconensis Poselger, Allg. Gartenz. 23: 18 (1855).
Neotype: About 20 km northeast of Saltillo, 22 July 1972, Edward F. Anderson 3180 (US 3050276), E.F. Anderson, Bradleya 5: 72 (1987).
Synonyms: Echinocactus rinconadensis Schumann, Gesambt. Kakt. 433 (1898). ?Echinocactus lophothele Salm-Dyck, Allg. Gartenz. 18: 395 (1850). Thelocactus lophothele Br. & R., Bull. Torrey Bot. Club 49: 251 (1922). Echinocactus phymatothelos Poselger ex Ruempler, in Förster, Handb. Cact., ed. 2, 602 (1885). Thelocactus phymatothelos Br. & R. ('phymatothele'), Cact. 4: 8 (1923). Thelocactus rinconensis var. phymatothelos Glass & Foster, Cact. Succ. J. (US) 49: 246 (1977). Thelocactus rinconensis ssp. phymatothele (Poselger) Glass, Ident. Guide Threatened Cacti of Mexico 1: TH/RIN (1997). Thelocactus rinconensis ssp. phymatothelos (Poselger) Doweld nom. superfl., Sukkulenty 1: 30 (1999). Thelomastus phymatothelos Frič, in Kreuzinger, Verzeichnis 10 (1935), nom. illeg. Thelocactus rinconensis ssp. icamolensis Halda & Kupcak, Acta Mus. Richnov. sect. Nat. 7: 75 (2000). Thelocactus lophothele ssp. rinconensis Matusz., Thelocactus 170 (2011).

Stem single, depressed or globose, 6-8 cm tall, 12-20 cm wide. Ribs >20, distinct. Tubercles conical, angled. Areoles without glands. Central spines 3-4, 60-80 mm long, ochre to greyish, acicular to subulate. Radial spines absent. Flowers 40-70 mm wide, white, yellowish or pink. Seeds 1.9 x 1.6 mm, testa cells tabular or slightly convex with a verrucose surface sculpture.

Mexico, Coahuila and Nuevo León, occurring in matorral xerofilo on limestone hills, at elevations of about 600 to 2000 metres above sea level. Its range lies within the Central Chihuahuan subregion of the Chihuahuan Desert ecoregion.

The species is characterised by its glaucous, depressed stem, divided into about twenty ribs and the presence of central spines only. All entities share sunken or globose stems, divided into many (about twenty) narrow ribs, blue-green, rarely green. The number and strength of the spines and the colour of the flowers, instead, are variable. The type species, Thelocactus rinconensis ssp. rinconensis, has a glaucous body, depressed or globose, with areoles bearing 3-5 central spines of variable length, while radial spines are absent. The flowers are usually white, sometimes pinkish. Thelocactus phymatothelos is closely related to this taxon, and I believe it is a local form not deserving its own formal status. It can be distinguished because the stem is always depressed, the spines are shorter and slightly curved, and the flowers are pink.

Icamolensis is a magenta flowering form occurring near Icamole, north-west of Monterrey. It has been first reported by Glass and Foster who related it to ssp. nidulans. The body shape and spination, 3-4 central spines, rather relates it to ssp. rinconensis, from which it differs only for the flower colour. This difference is too weak to recognize it at a separate rank.

Lophothele was described by Salm-Dyck in 1850, who probably based his description on the material brought by Potts in Europe in the same year, stating that the plant resembles a Mammillaria, but differing for the scaly ovary, a character relating it to Echinocacti. Scheer, in his chapter about cacteae in The botany of the voyage of H.M.S. Herald, tells us that John Potts was the manager of the mint at Chihuahua and that he collected plants from near the city or on short excursions from thence. Plants were sent almost annually to Scheer since 1842, while a large collection was brought in 1850 by Potts himself. The species was described as having a depressed body with a woolly apex, divided into 16 ribs. The tubercles bear 4 spines and two accessory upper spines, sometimes or frequently wanting. The flower was described in 1852 by Scheer in The botany of the voyage of H.M.S. Herald as having slightly fimbriate sepaloids and fleshy coloured petaloids with a purple midstrip.
Till now no plant matching the original description has been found in Chihuahua, therefore Glass and Foster considered it "little known and not necessarily referable to T. rinconensis, if indeed to Thelocactus", a conclusion with which later Anderson agreed. The fact is that botanists do not like discrepancies in the descriptions that may lead to confusion. Nevertheless it has usually been considered a form of rinconensis.
In 1851 Poselger visited La Rinconada during his Mexican field trip. In a note published in 1853, he referred this entity to E. lophothele, but in 1855 he changed his opinion and described it as E. rinconensis. Therefore, it seems likely that Poselger knew both taxa, and that he considered E. rinconensis sufficiently distinct from E. lophothele to deserve a new description.
This two species must have been considered very close by many, if even Schumann thought rinconensis was a variety of lophothele, the difference cleared to him by Mathsson. Finally, Schumann described lophothele as a clump-forming species, globose to short columnar, with 3-5 radial spines and occasionally one central spine, coming from Mariposa, which is close to La Rinconada, where was collected by Mathsson. Though I have still to see a clumping rinconensis, the two entities found at La Rinconada and at Mariposa must be the same species, and also if the description by Salm-Dyck may apply to them, the locality of origin of lophothele (Chihuahua) does not. You should remember that fide Scheer, Potts collected plants only in Chihuahua, therefore may be the original lophothele is still waiting to be rediscovered.
In 2011 G. F. Matuszewski and S. Hinz , after an extensive field work, concluded that the plants coming north of the highway Saltillo-Monterrey are identifiable with lophothele, while on the south rinconensis grows, the two differing for the spine count, 0-4 for rinconensis, 4-6 for lophothele, and the flower colour, white to pink in rinconensis versus yellowish in lophothele. They changed accordingly the nomenclature of this complex, combining all taxa under lophothele, which has priority over rinconensis. Right or not, we have now some more names to deal with.

Phymatothelos, which occurs south of Saltillo, is not sufficiently distinct to deserve its own formal status. It can be distinguished because the stem is always strongly depressed, the spines are shorter and slightly curved, and the flowers are pink.