Autor: (K. Brandegee) Walton

Because the genus (misspelled) is native to the region of the Cochimi Indians in Baja California, Mexico.
A genus of branched plants, many erect or prostrate elongated stems with distinct tubercles spirally arranged, not furrowed. Central spine hooked or straight (only in C. halei).
Flowers diurnal, self sterile, zygomorphic (bilaterally symmetrical), appearing in the axil of tubercles, bright red, pollinated by hummingbirds (Basilinnaxantusii, Caiypte costae). Fruits globular, naked, red to purple red, indehiscent. Seeds dark brown to black, pear-shaped, dotted with holes.
The genus Cochemiea grows endemically in the Baja California peninsula in Mexico at low altitudes near the ocean, often in full sun, but also in the shade of bushes, on rocky cliffs in canyons, on sandy or silty alluvial plains, or on hill slopes and rocky ridges, from sea level up to 1800 m in altitude.
Mexico (Baja California).
Currently 5 recognised species (or 3 species + 2 subspecies):
– Cochemiea halei* (K.Brandegee) Walton 1899
– Cochemiea maritima G.E.Lindsay 1937 (or C. pondil subsp. maritima)
– Cochemiea pondii* (Greene) Walton 1899
– Cochemiea poselgeri* (Hildm.) Britton & Rose 1923
– Cochemiea setispina* (J.M.Coult.) Walton 1899 (or C. pondii subsp. setispina)

References: "TAXONOMY of the CACTACEAE" -  ISBN 978-84-617-3723-9 (Vol. 1)