The staminate and pistillate flowers consist, respectively, of a single stamen and a single 3-carpellate pistil. These are arranged in a “false flower” or pseudanthium, in this genus called a cyathium, a cup-like structure or involucre in the center of which is a pistillate flower, on a stalk (the pedicel) that elongates as the fruit matures. Several staminate flowers surround the pistil, most easily interpreted as not merely stamens; if one notes the joint in the stalk of each, the portion below the joint corresponds to a pedicel and that above to a filament. Around the margin of the cyathium are (1–) 4–5 glands, and in some species these have petaloid appendages, so that the whole cyathium mimics a single flower. The milky juice is poisonous and for some people produces a dermatitis like that caused by poison-ivy.

1. Leaf blades distinctly asymmetrical at base; interpetiolar stipules present; plants annual, with opposite leaves and prostrate or erect habit.

2. Stems (at least the young internodes) ± pubescent (ranging from dense spreading hairs to a fine line of puberulence); leaf blades usually at least sparsely pubescent beneath when young.

3. Capsules and ovaries pubescent; stems with ± conspicuous mostly spreading hairs.

4. Plant erect; cyathia in dense peduncled axillary and terminal heads; blades of leaves acute, mostly at least 15 mm long.

E. hirta

4. Plant prostrate; cyathia solitary in axils but often on short axillary shoots; blades mostly obtuse or rounded, less than 12 (–14) mm long.

5. Capsules with appressed hairs evenly distributed over the whole surface; cyathial gland appendages present, white or pink, often crenate and slightly unequal; styles undivided for most their length; leaves narrowly elliptic-oblong, sparsely toothed for most of the length.

E. maculata

5. Capsules with erect hairs along the ridges, glabrous in between; cyathial gland appendages absent or a thin fringe along the glands; styles divided most of their length into two distinct branches; leaves broadly elliptic-obovoid, finely toothed mainly in distal half.

E. prostrata

3. Capsules and ovaries glabrous; stems often with only short incurved hairs.

6. Plant with erect stem and any main branches strongly ascending; largest leaf blades 16–27 (–33) mm long.

E. nutans

6. Plant branching from the base, widely spreading or prostrate; largest leaf blades less than 16 mm long.

E. vermiculata

2. Stem and leaves glabrous.

7. Leaves serrulate (sometimes weakly so) at least on apical third or half or along one side; mature seeds distinctly angled with shallowly pitted, rugulose, or ridged facets.

8. Seeds with 3–4 strong transverse ridges and furrows on each facet; leaf blades usually linear-oblong to slightly broader below the middle.

E. glyptosperma

8. Seeds with irregularly pitted or rugulose surface; leaf blades usually ± oblong to obovate.

E. serpyllifolia

7. Leaves completely entire (at most mucronate); seeds plump, rounded, smooth.

9. Seeds ca. 1.3–1.5 mm long; capsule ca. 1.5–1.8 mm long; cyathium with small petaloid appendages; leaf blades less than 2.5 (–3) times as long as wide.

10. Stipules of leaf pairs fused into a conspicuous flap of greenish tissue between the leaves, this often whitish-erose.

E. serpens

10. Stipules of leaves not united into a conspicuous flap, at most a thin ridge extending between the leaves, the stipules mostly represented by long, thin, flexuous, pinkish to straw colored fringes.

E. geyeri

9. Seeds ca. 2.4–2.7 mm long; capsule ca. 3–3.5 (–4) mm long; cyathium without petaloid appendages; leaf blades mostly 3.2–4.4 times as long as wide.

E. polygonifolia

1. Leaf blades essentially symmetrical at base; stipules absent; plants annual or perennial, with mostly alternate leaves (except sometimes the uppermost, subtending cyathia or rays of the inflorescence, and in E. davidii and E. dentata) and erect habit.

11. Cyathia with conspicuous white petaloid appendages on the glands.

12. Distal (and all) leaves without white borders, blunt; capsules and involucres glabrous or nearly so; perennials.

E. corollata

12. Distal leaves and bracts conspicuously white-bordered, with distinct mucro; capsules and involucres of cyathia pubescent; annuals.

E. marginata

11. Cyathia without petaloid appendages.

13. Inflorescence consisting of clusters of cyathia subtended by opposite leaves; cyathium bearing 1 large gland; cauline leaves distinctly toothed, all or mostly opposite, ± antrorsely scabrous-pubescent; stem ± retrorsely scabrous-pubescent.

14. Underside of leaves with relatively stiff hairs that are conspicuously widened at the base.

E. davidii

14. Undersides of leaves with soft hairs that are ± the same width most of their length (only slightly widened at the base, i.e., ± cylindrical), except near the apex.

E. dentata

13. Inflorescence consisting of umbellate rays subtended by a whorl of leafy bracts; cyathium bearing 4 glands; cauline leaves finely toothed or entire, all alternate, glabrous or at most loosely villous; stem glabrous or loosely villous.

15. Leaves minutely toothed, at least on part of their margins; glands of cyathium rounded to obscurely reniform.

16. Capsules smooth (except as dried over reticulate seed); seeds with strong raised reticulate pattern; principal inflorescences consisting of 5 umbellate rays and cyathia glabrous on the outside.

E. helioscopia

16. Capsules tuberculate with prominent papillae; seeds smooth; principal inflorescences consisting of 3 rays or cyathia pubescent on the involucre.

17. Leaves and outside of cyathia glabrous; rays of principal inflorescences 3; leaf apex obtuse.

E. spathulata

17. Leaves beneath (at least along midrib) and outside of cyathia ± loosely villous; rays of principal inflorescences usually 5; leaf apex abruptly acute.

E. platyphylla

15. Leaves strictly entire; glands of cyathium crescent-shaped, with pointed tips or even prolonged horns.

18. Leaf blades ± rotund to obovate, less than 3 times as long as wide; seeds conspicuously pitted; annuals, with usually 3 primary rays in the inflorescence.

19. Seeds with numerous uniform small pits narrower than the ridges between them; bracteal leaves of inflorescence slightly broader than long.

E. commutata

19. Seeds with few large pits broader than the ridges between them (1 on each ventral facet, 2–4 on each dorsal facet); bracteal leaves slightly longer than broad.

E. peplus

18. Leaf blades linear to lanceolate, (6–) 8–15 (–18) times as long as wide; seeds smooth; perennials, with more than 5 rays in inflorescence.

20. Main cauline leaf blades all less than 2.5 (–3) mm broad; floral bracts (not those at base of rays) 3–6 (–7) mm wide.

E. cyparissias

20. Main cauline leaves 3.2–10 (–15) mm broad; floral bracts (at least the largest) 8–16 (–27) mm wide.

E. virgata