51. Borrichia. Achenes 3–4-angled; pappus a short 4-toothed crown. Shrubby.

52. Helianthus. Achenes flattened, bearing 2 very deciduous chaffy pointed scales.

[=][=][=] Receptacle convex (rarely conical). Achenes flat-compressed laterally, winged or wingless, 2-awned. Leaves decurrent.

53. Verbesina. Involucral scales closely imbricated in 2 or more rows.

54. Actinomeris. Scales few, soon deflexed. Achenes obovate, squarrosely spreading.

[*] 4. Rays few, neutral, or wanting. Achenes obcompressed, i.e., flattened parallel with the scales of the involucre (rarely terete). Involucre double; the outer spreading and often foliaceous. Receptacle flat. Leaves opposite.

55. Coreopsis. Pappus of 2 (or rarely more) scales, teeth, or awns, which are naked or barbed upward, sometimes obsolete or a mere crown.

56. Bidens. Pappus of 2 or more rigid and persistent downwardly barbed awns or teeth.

57. Thelesperma. Inner involucre connate to the middle. Achenes terete. Awns retrorsely bearded.

[*] 5. Heads radiate or discoid; disk-flowers all perfect and fertile. Achenes turbinate, 5-angled; pappus of several chaffy scales.