Probably from Aria (now Sorbus) and Greek karpos — fruit, referring to a perceived similarity of fruits of the two genera.
Low-growing body consisting of a cone-like rosette of thick more or less spineless tubercles. Rootstock thick. Spines mostly absent. Tubercles sometimes with a felted grove above or naked or with a rounded areole near the tip. Flowers funnel-shaped, pink, purple, pale yellow or white; late summer to autumn. Pericarpel and flower tube usually concealed, naked. Fruit inconspicuous, round to club-shaped, fleshy at first but becoming dry.
The species keyed out below are largely collectors items.
Thickened rootstock; tubercles thick, more or less spineless, spreading, in a cone-like rosette. Some species with felted groove on tubercles, like Coryphantha.
6 species from N & E Mexico and S Texas.
Source: (1997). Cactaceae. In: . Horticultural Flora of South-eastern Australia. Volume 2. Flowering plants. Dicotyledons. Part 1. The identification of garden and cultivated plants. University of New South Wales Press.