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Keyed in multiple places:

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Key to Cyperus, Key E: Key to subgenus Cyperus – stigmas 3; achenes trigonous; spikelets borne in spikes on a well-developed rachis;
rachilla continuous, or articulate only at the base

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1 Leaf blades absent; culms 15-50 mm thick, nearly terete; inflorescence open and diffuse, primary rays 10-30 cm long, bearing numerous 2nd and 3rd order rays up to 20 cm long and bracts to 25 cm long, often drooping; anther connectives subulate, projected beyond the anther 0.2-0.5 mm; [exotics, commonly cultivated, rarely naturalizing]; [subgenus Cyperus, section Papyrus]
..2 Rays stiff, ascending to erect; primary bracts (8-) 20-45 cm long
..2 Rays slender, drooping or arching; primary bracts 3-8 cm long
1 Leaf blades well-developed (except C. articulatus); culms < 20mm thick, trigonous if broader than 5 mm; inflorescence smaller, more congested (except C. prolixus); anther connectives not prolonged.
....3 Spikelets quadrangular to subterete, 1-1.5× as wide as thick; floral scales 1-8, persistent and tightly appressed (rarely slightly ascending); rachilla articulate at the base, the whole spikelet falling as a unit at maturity
....3 Spikelets compressed-quadrangular or compressed-subterete, mostly 2× or more as wide as thick (less compressed in C. erythrorhizos and some forms of C. esculentus and C. rotundus); scales 1-many, deciduous or persistent; rachilla persistent or deciduous after the scales.
......4 Spikes long-cylindric, with (25-) 35-80+ spikelets, and well-developed branches or 2nd order rays; scales deciduous, minute, (1.1-) 1.3-1.8 mm long, (6-) 12-20 (-30) per spikelet; spikelets quadrangular, slightly compressed (subterete in C. alopecuroides); achenes (0.4) 0.7-1 (-1.2) mm long, often moderately dorsiventrally compressed or plano-convex; plants coarse perennials, culms 5-25 dm tall, 5-50 mm in diameter (C. erythrorhizos keyed under both leads).
........5 Stigmas 2, or 2 and 3 on a plant; spikes narrowly cylindric, the rachis obscured by the densely packed, ascending, imbricate spikelets; spikelets subterete, somewhat compressed, ovoid to oblong; rachilla wings absent to 0.1 mm wide; achene lenticular, its face against the rachilla [rare waif, FL]; [section Alopecuroides]
........5 Stigmas 3; spikes less dense, spikelets spreading to divaricate; spikelets quadrangular, linear; rachilla winged, wings 0.3 mm wide; achenes not as above [collectively widespread]; [section Fastigiati].
..........6 Plants perennial, with indurate rhizomes (sometimes inconspicuous); roots not reddish; floral scales 1.6-1.8 mm long; anthers 0.4-0.5 mm long; culms robust, trigonous, 5-25 dm tall, 5-15 mm wide
..........6 Plants annual; roots reddish, fibrous; floral scales 1.3-1.5 mm long; anthers 0.2-0.3 mm long; culms shorter, mostly rounded, (0.05-) 0.5-2.5 (-10.5) dm tall, 1-7.5 mm wide
......4 Spikes not as above; scales persistent or deciduous, mostly > 1.8 mm long (except sections Iriodei and Aristati); achenes > 1 mm long, trigonous (dorsiventrally compressed in C. nipponicus and C. serotinus); culms mostly < 10 dm tall, < 7.5 mm in diameter (except C. prolixus).
............ 7 Spikelets 1.2-1.5 (-1.6)mm wide, only compressed proximally, filiform distally; adjacent scales spaced apart on the same side of the rachilla; rachilla wings absent or very reduced; [subgenus Cyperus, section Distantes]
............ 7 Spikelets mostly broader, not filiform distally; scales apices reaching or exceeding the base of the next scale on the same side of the rachilla; rachilla wings present or absent.
............ ..8 Scales strongly 5-nerved, obovate-orbiculate, 1-1.5 mm long, divaricate, scarcely overlapping, apex emarginate and mucronulate; style < 0.1 mm long; inflorescence diffuse, secondary rays present, spikelets widely spaced on elongate rachises; [weedy exotics]; [section Iriodei]
............ ....9 Mucro ≤ 0.12 mm long; spikelets appressed to erect-ascending
............ ....9 Mucro 0.2-0.3 mm long; spikelets divaricate
............ ..8 Scales variously nerved, but at least 1.8 mm long (if shorter, with an excurved cusp > 0.5 mm long), not emarginate; style at least 0.5 mm long; inflorescence generally more congested.
............ ......10 Scales cuspidate to awned, midrib excurrent at least 0.3 mm, conspicuously excurved (straight in C. compressus and C. nipponicus); plants either diminutive fibrous-rooted annuals, culms often decumbent, or cespitose perennials (section Elegantes) with involute leaves and vegetative parts viscid (sticky).
............ ......10 Scales acute, midrib not notably projecting, apices not excurved; plants erect, rhizomatous, stoloniferous, cormose-based, or cespitose perennials, vegetative parts not viscid, leaves plane or V-shaped (cuspidate perennial species also keyed above).
............ ........11 Stigmas 2; achenes dorsiventrally compressed; spikelets subterete, elliptic in ×-section; [subgenus Juncellus, section Stoloniferi]

Key to Cyperus, Key ZE: Key to Cyperus, subgenus Cyperus of various affinities -- Spikelets compressed; scales deciduous or persistent; rachilla persistent or deciduous after the scales

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1 Culms and leaves bluish-glaucous in life; scales overlapping, slightly spreading, glossy reddish brown at maturity; plants cespitose perennials; [FL; beaches, dunes, coastal rock]
..2 Rays absent, inflorescence a single globose spike, rachis only 1-3 mm long; scales 1.5-2.2 mm long; achenes 1-1.2 mm long, glabrous, puncticulate, or papillose; leaves and bracts 1-2.5 mm wide; culms 0.5-1 mm in diameter; [section Laxiglumi]
..2 Rays present, inflorescence of multiple well-developed spikes, though often very congested; scales 2.5-3 mm long; achenes 1.3-2 mm long, coarsely punctate; leaves and bracts (1.5-) 3-10 mm wide; culms 0.8-2.6 mm in diameter; [section Thunbergiani]
1 Culms and leaves green, not glaucous; scales divaricate to closely imbricate, mostly greenish, light brown, or straw-colored (except C. rotundus and C. setigerus); [more widespread].
....3 Rachilla wingless (except C. prolixus and C. grayi); spikelets at maturity 2-4 mm wide, scales divaricate (the spikelet appearing coarsely serrate in outline).
......4 Rachis hispidulous; spikes loosely oblong-ovoid, with spikelets spreading, the elongate, well-developed rachis clearly visible; scales 1.8-2 mm long, light brown to yellowish; achenes 1-1.2 mm long; [sect. Proceri]
......4 Rachis glabrous; spikes densely ovoid or globose, or umbellate to oblong, the rachis elongate to nearly absent; scales 1.8-3.2 mm long; achenes 1.5-2.4 mm long (1-1.2 mm long in C. cephalanthus).
........5 Rays compressed; plants robust, up to 2m tall; inflorescence diffuse, 2nd-order rays present, erect, 1-10 cm long, usually bearing well-developed 3d-order rays 0.5-5 cm long; [sect. Distantes]
........5 Rays terete to trigonous; plants mostly less robust, to 1m tall; inflorescence more compact, 2nd- and 3rd-order rays absent or poorly developed.
..........6 Plants robust, culms 40-100 cm tall, sharply trigonous, scabrid to hirtellate on the angles; spikes very densely ovoid, with 25-50+ spikelets, subtended by well-developed secondary bracts and often branched at the base; achenes 1.0-1.2 mm long, ellipsoid, <1/2 as long as the scales; [coastal prairies; LA, TX]; [sect. Thunbergiani]
..........6 Plants smaller, culms to 50 cm tall, terete to trigonous, not scabrid (except C. schweinitzii); spikes relatively loose, with 3-24 spikelets, unbranched and lacking secondary bracts; achenes 1.5-2.2 mm long, mostly ≥ 1/2 as long as the scales; [dry, sandy or rocky soils; collectively widespread]; [sect. Laxiglumi].
............ 7 Inflorescence bracts deflexed (to horizontal); spikelets in a single sessile hemispheric to globose capitate cluster, or with an additional 1-4 smaller pedunculate spikes, these densely globose with an obscure rachis < 6 mm long; [Cyperus lupulinus complex]
............ ..8 Anthers 0.8-1 mm long; achenes 0.5-0.8 mm wide, narrowly oblong; scales usually yellowish to yellowish brown; leaves very narrow, 0.5-2 mm wide
............ ..8 Anthers 0.3-0.6 mm long; achenes 0.8-1.2 mm wide, ±ellipsoid; scales usually off-white to pale tan to light reddish brown; leaves often broader, 1-4 mm wide.
............ ....9 Scales 2.5-3.8 mm long, usually fitting loosely over the mature achene, the margins spreading or loosely clasping it; spikelet with 5-22 scales
............ ....9 Scales 1.8-2.5 mm long, usually fitting tightly over the achene, the margins tightly clasping it; spikelets with 3-7 scales
............ 7 Inflorescence bracts horizontal to erect; spikes primarily pedunculate, loosely globose, densely ovoid, or more elongate.
............ ......10 Scales 2.2-3.2 mm long with a conspicuous cusp > 0.3 mm long (at least on the distal scales); body of scale 2.2-3.2 mm long; spikes umbellate to oblong, spikelets all erect-ascending; achenes 2-2.4 mm long, ellipsoid; plants rhizomatous, culms sharply trigonous
............ ......10 Scales 1.3-2.5 mm long, acute or minutely mucronate (mucro ≤ 0.2mm long); spikes mostly globose or ovoid, spikelets usually spreading or radiating in all directions (erect-ascending in C. houghtonii); achenes 1.5-2.4 mm long; plants various.
............ ........11 Spikelets mostly erect-ascending, the spikes umbellate to broadly ovoid; scales with distinct mucro 0.1-0.2 mm long; achenes 1-1.5 mm wide, broadly ellipsoid; anthers 0.5-0.7 mm long
............ ........11 Spikelets radiating in all directions, the spikes globose or subglobose; scales acute; achenes 0.7-1.2 mm wide, narrowly ellipsoid or oblong-ellipsoid; anthers 0.7-1.2 mm long.
............ ..........12 Rachilla winged, wings 0.6 mm wide; achenes 1.5-2 mm long × 0.7-1 mm wide; scales 2-2.8 mm long; anthers 0.7-1 mm long; [Atlantic coast, south to AL]
............ ..........12 Rachilla wingless; achenes 2-2.4 mm long × 0.9-1.2 mm wide; scales 2.5-3 mm long; anthers 1-1.2 mm long; [Midwest south to LA]
....3 Rachilla winged, wings at least 0.4 mm wide; spikelets at most 2.2 mm wide, scales overlapping, tips closely imbricate, the margin appearing smooth or slightly serrate (some forms of C. strigosus have looser scales).
............ ............ 13 Scales 1-1.5 mm long, deciduous; spikes cylindric, with (20-) 40-80+ spikelets, often with secondary rays; fibrous-rooted annuals, but often robust, roots reddish; [sect. Fastigiati]
............ ............ 13 Scales 1.8-4.5 (-6) mm, deciduous or persistent; spikes ovoid, with (2-) 3-50 spikelets; stoloniferous, rhizomatous, cormose-based, or (C. sphacelatus) cespitose perennials.
............ ............ ..14 Plants with cormose culm bases; scales 3.2-4.5 (-6) mm, 3-11 per spikelet, pale greenish-brown to straw-colored, dull; spikelets strongly compressed (at maturity), the scales loosely overlapping, tips spreading; achenes narrowly oblong, (1.5-) 1.8-2.4 mm long; [section Strigosi]
............ ............ ..14 Plants lacking cormose culm bases; scales 1.8-4 (-4.4) mm long, 6-36 (-42) per spikelet, various; spikelets often only slightly compressed, scales closely imbricate, tips appressed; achenes ellipsoid to oblong, 1.1-2 mm long.
............ ............ ....15 Scales pale greenish-white, deciduous, usually with dark-speckled margins visible as a prominent dark line on each side of the spikelet; plants fibrous-rooted; anthers 0.6mm long, styles 0.6-1.2 mm long, stigmas 1-1.4 (-1.7) mm long; [rare introduction, FL]; [section Subimbricati]
............ ............ ....15 Scales pale yellowish to brown or deep purple, persistent or deciduous; plants with well-developed rhizomes or stolons; anthers 1-2.5 mm long, styles (0.7-) 1-3.6 mm long, stigmas (1.2-) 1.8-6 mm long; [collectively widespread]; [section Cyperus].
............ ............ ......16 Culms terete at least towards the base, nodose-septate, with internal partitions every 5-50 mm, more frequent upwards; leaves usually all reduced to bladeless sheaths; bracts 2 (-4), erect, reduced, mostly < 2 cm long
............ ............ ......16 Culms trigonous to rounded-trigonous, not nodose-septate; leaf blades present; bracts (2-) 3-8, spreading to ascending, well-developed.
............ ............ ........17 Scales deciduous, (2.2-) 2.7-4.5 (-6) mm, mostly reddish-brown; robust perennials 5-10dm tall from thick, indurate rhizomes, lacking tubers; achenes maturing, oblong
............ ............ ........17 Scales persistent, 1.8-3.4 mm long, mostly yellowish or dark glossy purplish; plants mostly 1-6 dm tall (rarely taller in C. esculentus), with slender stolons 1-2 mm in diameter, these producing terminal tubers; achenes ellipsoid or not maturing.
............ ............ ..........18 Spikelets (2-) 3-14 per spike, bracts often not exceeding the inflorescence; scales glossy dark purplish, with green keels and hyaline border; culm bases indurate, stolons wiry, horizontal, 1-2 mm in diameter, producing irregular, often elongate tubers
............ ............ ..........18 Spikelets (3-) 10-28 per spike, bracts exceeding the inflorescence; scales yellowish to dull reddish-brown; culm bases not indurate, stolons spongy, weak, 1 mm in diameter, producing globose tubers; [Cyperus esculentus complex].
............ ............ ............ 19 Spikelets ascending-erect; floral scales deltate-ovate, widest 1/4-1/3 of the way from the base
............ ............ ............ 19 Spikelets spreading; floral scales ovate to ovate-lanceolate, widest near the middle.
............ ............ ............ ..20 Style and stigma combined < 4.2mm long; floral scales 1.8-2.7 mm long; anthers (1-) ca. 1.3 (-1.6) mm long
............ ............ ............ ..20 Style and stigma combined > 4.2mm long; floral scales (2.7-) 2.9-3.4 mm long; anthers (1.2-) 1.3-2.1 mm long
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