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Key to Rhynchospora, Key F: beaksedges with bristles smooth, or antrorsely barbed and filiform, or absent,
the achene surface transversely ridged, rugose, or honeycombed-reticulate
[subgenus Diplostylae; sections Globulares, Harveyae, Mixtae, Psilocarya, Pusillae, Rariflorae]

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1 Bristles absent (or apparently so at 10×); achene 0.5-0.7 mm wide; tubercle 0.1-0.2 mm long, skull-cap like; [section Pusillae].
  2 Achene including tubercle 1.0-1.2 mm long, the achene surface evidently reticulate and obscurely transversely ridged, the body ellipsoid; bristles present, white, barely visible at 20×, the longest shorter than the achene body
  2 Achene including tubercle 0.6-0.9 mm long, the body obovoid; bristles absent.
    3 Achene surface smooth, faintly reticulate, not transversely ridged
    3 Achene surface rough, distinctly transversely ridge
1 Bristles present or absent; if absent, then the achene > 1 mm long or > 0.7 mm wide, and tubercle triangular to subulate.
      4 Culms and leaves filiform.
        5 Achene including tubercle 1.0-1.2 mm long; tubercle minute, skullcap-like; [section Pusillae]
        5 Achene including tubercle 1.5-2.9 mm long; tubercle triangular to triangular-acuminate; [section Rariflorae].
          6 Bristles subequaling to exceeding the tubercle; tubercle 0.75-1.4 mm long
          6 Bristles shorter than the achene body; tubercle 0.3-1.0 mm long.
             7 Achene 1.3-1.6 mm long, 0.9-1.4 mm wide; tubercle 0.3-0.6 (-0.75) mm long; bristles 1/3-1/2(-4/5) as long as achene body
             7 Achene 1.6-1.8 mm long, 1.35-1.5 mm wide; tubercle 0.6-1.0 mm long; bristles 2/3 to nearly as long as achene body
      4 Culms stouter; leaves wider, not filiform.
               8 Achene faces flat or concave; when one face is concave, the opposite face is sometimes slightly convex (slightly biconvex R. decurrens and R. microcarpa are keyed here for convenience).
                 9 Achene at least twice as long as wide, elliptic-oblong; tubercle subulate, 0.8-1.2 mm long; [section Mixtae]
                 9 Achene < twice as long as wide, obovate; tubercle triangular, 0.2-0.9 mm long.
                   10 Longer bristles exceeding the achene body.
                     11 Achene ±2.2 mm long, ±1.8 mm wide; tubercle ±0.9 mm long; [section Globulares]
                     11 Achene 0.8-1.2 mm long, 0.7-1.2 mm wide; tubercle 0.2-0.5 mm long; [section Mixtae].
                       12 Larger leaves (3-) 4-6 mm wide; bristles exceeding tubercle; achene faces flattened
                       12 Larger leaves 1-3 (-4) mm wide, bristles half as long as achene to equaling tubercle; achene faces slightly convex
                   10 Longer bristles shorter than to equaling achene body, or absent.
                          13 Larger leaves 3-5 mm wide; achene 1.4-1.6 mm wide; tubercle 0.6-0.8 mm long, abruptly rising from a flaring basal collar; [section Globulares]
                          13 Larger leaves 1-3 (-4) mm wide; achene 0.7-1.3 mm wide; tubercle 0.15-0.5 mm long, without a flaring basal collar; [section Mixtae].
                            14 Bristles evident, at least 1/4 as long to exceeding achene.
                              15 Culms 20-50 cm long; leaves 1-2 mm wide; bristles ½ or less as long as achene body
                              15 Culms 50-110 cm long; leaves (1-) 2-4.5 mm wide; longer bristles more than ½ as long to exceeding achene body.
                                16 Achene 1.3-1.8 mm long, 0.9-1.2 mm wide, the faces flat with 10-12 transverse ridges
                                16 Achene 0.8-1.4 mm long, 0.7-1.2 mm wide, the faces slightly biconvex with 6-12 transverse ridges.
                                  17 Clusters elongate; achene 1.0-1.4 mm long, 0.8-1.0 mm wide, narrowly obovate to elliptic, averaging 8-12 transverse ridges; most tubercle bases convexly seated on the achene summit and somewhat decurrent along the achene margins, the tubercle surface often whitish-waxy
                                  17 Clusters usually compact; achene 0.8-1.2 mm long, 0.7-1.2 mm wide, suborbicular to elliptic, averaging 6-7 transverse ridges; most tubercle bases flat across the achene summit, not decurrent, the tubercle surface usually dark, not waxy
                                    18 Achene 1.4-4.2 mm long, 1.2-3.6 mm wide, the summit with a thickened bony to crustaceous rim surrounding the base of the tubercle; [section Harveyae].
                                       19 Achene tumid, lightly pitted or cancellate in a honeycomb pattern, 1.5-4.2 mm long, 1.4-3.6 mm wide.
                                    18 Achene 0.7-1.8 mm long, 0.7-1.5 mm wide, the summit without a textured rim surrounding the base of the tubercle (if the base of the tubercle is rim-like, then it is distinguished from the summit of the achene by a constriction or articulation).
                                                 24 Spikelets (5-) 6-10 mm long, tan or brown, with an acuminate tip; tubercle ends upturned away from the achene at about a 90 degree angle
                                             22 Bristles present (occasionally detached in R. decurrens and R. miliacea with achenes 1.0-1.4 mm long); achene 0.8-1.9 mm long.
                                                      26 Cluster branches flexuous; bristles one-half as long to equaling the achene (or longer in R. microcarpa); [section Mixtae].
                                                        27 Clusters elongate; spikelets 2.5-3.5 mm long; achene narrowly obovate to elliptic, averaging 8-12 transverse ridges; most tubercle bases convexly seated on the achene summit and somewhat decurrent along the achene margins, the tubercle surface often whitish-waxy
                                                        27 Clusters usually compact; spikelets 1.5-3.0 mm long; achene suborbicular to elliptic, averaging 5-8 transverse ridges, most tubercle bases flat across the achene summit, not or only slightly decurrent, the tubercle surface usually dark, not waxy.
                                                          28 Inflorescence occupying the upper ¼-½ of the culm, the lowest 2-4 nodes barren; spikelets 2.0-3.0 mm long, ovoid, acute; achene body averaging (7-) 8 horizontal ridges; tubercle 0.25-0.85 mm long
                                                          28 Inflorescence occupying the upper 2/3-3/4 of the length of the culm, the lowest lateral panicle at the first or second node above the base; spikelets 1.5-2.25 mm long, broadly ovoid to suborbicular, apically rounded; achene body averaging 5-6 (-7) horizontal ridges; tubercle 0.2-0.4 mm long
                                                      26 Cluster branches stiff, bristles < 1/3 to ¾ (-1) × as long as achene body; [section Globulares].
                                                              30 Larger culm leaves to 5 mm wide; achenes (1.2-) 1.4-1.6 (-1.9) mm long, (1.1-) avg. 1.4 (-1.75) mm wide; achene surface alveoli longitudinally narrow; tubercle 0.3-0.7 mm long, base 0.6-1.0 mm wide
                                                              30 Larger culm leaves to 3 mm wide; achenes (1.0-) avg. 1.3 (-1.5) mm long and wide; if achene surface alveoli longitudinally narrow, then tubercle 0.2-0.4 mm long and base 0.5-0.7 mm wide (R. globularis).
                                                                 31 Longer bristles ⅓-½ (-¾)× the length of the achene; achene surface alveoli longitudinally narrow (typically 0.02-0.05 mm wide between the longitudinal walls), the latitudinal walls raised into horizontal ridges; tubercle 0.2-0.4 mm long, the base 0.5-0.7 mm wide
                                                                 31 Longer bristles ⅔-1× the length of the achene; achene surface alveoli nearly as wide as long (typically 0.05-0.1 mm wide between the longitudinal walls), the latitudinal walls obscurely or not at all raised into horizontal ridges; tubercle 0.35-0.7 mm long, the base 0.7-0.9 mm wide
                                                                   32 Primary branches of the inflorescence spreading at right angles from the culm, each spikelet or small cluster on slender spreading or reflexed stalks; [section Mixtae]
                                                                       34 Tubercle 0.4-0.8 mm long, the edges setose or uneven with waxy or crusty irregular protuberances; [section Mixtae].
                                                                           36 Spikelets 2.5-3 mm long; longer bristles about equaling the tubercle; achene 0.8-1.2 mm long, 0.7-1.2 mm wide; [section Mixtae].
                                                                              37 Inflorescence occupying the upper ¼-½ of the culm, the lowest 2-4 nodes barren; spikelets 2.0-3.0 mm long, ovoid, acute; achene body averaging (7-) 8 horizontal ridges; tubercle 0.25-0.85 mm long
                                                                              37 Inflorescence occupying the upper 2/3-3/4 of the length of the culm, the lowest lateral panicle at the first or second node above the base; spikelets 1.5-2.25 mm long, broadly ovoid to suborbicular, apically rounded; achene body averaging 5-6 (-7) horizontal ridges; tubercle 0.2-0.4 mm long
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