1	"Stem regularly segmented; areoles with glochids; seeds tightly encased within bone-like aril, +- white when dry"	2
1	"Stem not regularly segmented; glochids 0; dry seeds generally black to +- red-brown, lacking a +- white bone-like aril"	4
2	"Stem segments flat, tubercles 0 to +- developed; spine surface not separating"	Opuntia
2	"Stem segments cylindric to club-like, generally tubercled; spine surface sheath-like, generally separating and late-deciduous"	3
3	"Spines not flat; spine sheath 0 or fully separating; mature plant generally 0.3--4 m"	Cylindropuntia
3	"Major spines flat; spine sheath separating only from tip; mature plant generally < 0.25 m"	Grusonia
4	"Largest spines with transverse ridges; spines generally 2--5 mm diam near base, rigid"	5
4	"Largest spines smooth or longitudinally ridged; spines generally < 2 mm diam near base, rigid or not, thin, flexible if > 2 mm wide"	6
5	"Ovary, generally stem tip densely woolly, obscuring epidermis, ovary scales tapered to sharp tips"	"Echinocactus {Echinocactus polycephalus var. polycephalus}"
5	"Ovary, stem tip glabrous, only areoles woolly, ovary scales generally rounded"	Ferocactus
6	"Stem ribs 0 or inconspicuous, tubercles prominent"	7
6	"Stem ribs prominent, tubercles +- 0 or prominent on ribs"	8
7	"Spines all straight to +- curved; stem tubercles with woolly, adaxial groove connecting spine cluster to axillary flower areole"	Coryphantha
7	"Some spines in each areole generally hook-shaped; stem tubercles not adaxially grooved"	Mammillaria
8	"Stem > 30 cm diam, branched but generally not in basal 1.5--2 m; perianth generally white"	"Carnegiea {Carnegiea gigantea}"
8	"Stem < 15 cm diam, not branched, or branched in basal 1.5 m; perianth variously colored, but generally not white"	9
9	"Stem length > 8 &times; diam; fruit persistent when empty, densely spiny; coastal"	"Bergerocactus {Bergerocactus emoryi}"
9	"Stem length < 6 &times; diam; fruit not persistent when empty, spineless or spines deciduous; inland"	10
10	"Flowers lateral; ovary minutely scaly, spiny, spines deciduous in clusters; stem soft-fleshy, branches 1--500"	Echinocereus
10	"Flowers at stem tip or nearly so; ovary scaly, spineless; stem +- hard, branches 0--few (more if stem damaged)"	Sclerocactus