A. Joints all terete, elongated or short, cylindric to globose.
B. Branches several, many-jointed Subgenus 1. Cylindropuntia
C. Spines with papery sheaths.
D. Spines, at least some of them, solitary, sometimes several, acicular;
ultimate branches slender, rarely more than 1 cm. thick.
E. Stem and branches conspicuously marked by flattened, diamond-shaped tubercles; fruit dry, covered with long bristle-like spines Series 1. Ramosissimae (N. A.
EE. Tubercles not flattened nor diamond-shaped; fruit usually a naked berry Series 2.
DD. Spines always more than 1; ultimate branches stouter.
E. Ultimate branches not over 2 cm. thick Series 3.
EE. Ultimate branches 2 cm. thick or more.
FF. Fruit fleshy.
G. Tubercles of young joints scarcely longer than broad . . Series 5.
GG. Tubercles distinctly longer than broad.
H. Tubercles narrow, high, laterally flattened Series 6.
HH. Tubercles broad, low Series 7.
CC. Spines without sheaths.
D. Joints not tuberculate, or with broad or flat tubercles.
E. Areoles long-woolly or with weak hairs (without hairs in O. verschaffeltii) Series 8. Vestitae (S. A.)
EE. Areoles neither long-woolly nor long-hairy.
F. Joints clavate or crested Series 9. Clavarioides (S. A.)
FF. Joints neither clavate nor crested.
G. Low, slender species, scarcely, if at all, tuberculate . . . . Series 10. Salmianae (S. A.)
G. Tall, stout species, the tubercles broad or flat;
leaves large Series 11. Subulatae (S. A.)
DD. Joints strongly tuberculate, the tubercles elevated.
E. Tall, shrubby species; joints cylindric Series 12. Miquelianae (S. A.)
EE. Low, prostrate species; joints clavate (transition to
Tephrocactus) Series 13. Clavatae (N. A.)
BB. Branches 1 to few-jointed, the short joints usually clustered Subgenus 2. Tephrocactus (S. A.)
C. Joints, at least some of them, cylindric, tuberculate, the tubercles contiguous (transition to Cylindropuntia) . . . Series 1. Weberianae CC. Joints globose to oblong, mostly little, if at all, tuberculate.
D. Areoles normally bearing many long white hairs, which often cover the whole plant Series 2. Floccosae
DD. Areoles without hairs.
E. Spines, when present, at least some of them, modified into flat, papery processes Series 3. Glomeratae
EE. Spines, when present, all subulate or acicular, terete or somewhat flattened Series 4. Pentlandianae
Thurberianae (N. A.)
Echinocarpae (N. A.)
Bigelovianae (N. A.)
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