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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 ZC: Key to Cyperus, subgenus Pycnostachys, sections Fusci, Diffusi, and Haspani -- Spikelets in digitate clusters or glomerulate heads; scales broadly rounded or conduplicate

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1 Scales orbiculate or broadly obovate, to 1.1 mm long and wide, about as broad as long, minutely mucronate at the tip (“bead-like”); achenes 0.6-0.9 mm long × 0.3-0.4 mm wide, not much exceeded by the scales; plants fibrous-rooted annuals; [sect. Fusci]
..2 Heads very dense, spikelets 30-120 per head; scales 0.6-0.8 mm long × 0.6-0.8 mm wide, greenish; styles 0.1 mm long
..2 Heads looser, spikelets 3-12 per head; scales 0.9-1.1 mm long × 1 mm wide, light brown, bronze, whitish, or purplish brown; styles 0.3-0.4 mm long
1 Scales ovate to lanceolate, (1.1-) 1.6 mm long or longer, mucronate or not; achenes, if < 1.5 mm, much exceeded by (<1/2 the length of) the scales; plants perennial, often with cormose bases, stolons, or rhizomes.
....3 Leave involute; live plants viscid; scales with a mucronate to cuspidate apex at least 0.2 mm long, usually excurved; achenes with beaks 0.5-1.2 mm long or a whitish overlay and spongy stipitate base; [subgenus Cyperus, section Elegantes; keyed here as failsafes]
....3 Leaves flat or V-shaped; live plants not viscid; scales obtuse to acute (minutely mucronate in C. dentatus); achenes at most 1 mm long (longer in the obscurely spicate subg. Cyperus species keyed here as failsafes), without a beak or spongy stipitate base.
......4 Bracts large and conspicuous, 7-11, lanceolate, 5-25 mm wide, the main veins whitish-banded adaxially; inflorescence open and diffuse, often with 2nd and 3rd order rays; [cultivated, rarely naturalizing]; [section Diffusi]
......4 Bracts usually < 7, linear, < 10 mm wide, without whitish banding on the main veins, shorter than the culm.
........5 Spikelets in dense spikes, inflorescence often capitate; scales divaricate at maturity, rounded on the keel, weakly 5-13-nerved; achenes (1-) 1.4-2.5 mm long; plants mostly with hardened cormose culm bases, sometimes also rhizomatous; [dry, sandy habitats]; [subgenus Cyperus, section Laxiglumi; keyed here as failsafes].
........5 Spikelets in loose digitate clusters, rays elongate (except some forms of C. haspan); scales closely appressed, conduplicate and weakly 1-3 (-5)-ribbed; achenes 0.3-1 mm long; plants stoloniferous or rhizomatous; [mostly in wetlands]; [section Haspani]
..........6 Leaf blades usually absent; bracts 2 (-4), usually much reduced; achenes 0.3-0.6 mm long, globose to obovoid.
............ 7 Rays 5-15; anther 1-1.2 mm long; culms hard, not much flattening in pressing; [native]
............ 7 Rays 200-300; anthers 0.3-0.5 mm long; culms soft, terete, flattening in pressing; [cultivated, rarely naturalizing]
..........6 Leaf blades present; bracts 3-5, well-developed and often exceeding the inflorescence; achenes 0.7-1 mm long.
............ ..8 Scales 2-2.5 mm long × 1.2-2 mm wide, ovate or broadly elliptic, 3-26 (-50) per spikelet, minutely mucronate, sometimes excurved; spikelets ovate to linear, straight, light brown to reddish-brown laterally with greenish midribs; plants with stolons terminated by tubers, and often proliferous spikelets
............ ..8 Scales 2.5-3 mm long × 1-1.8 mm wide, relatively narrowly ovate-elliptic, 20-60 per spikelet, blunt and incurved; spikelets lanceolate to linear, often contorted, pale yellowish at maturity; plants with stolons, lacking tubers or proliferous spikelets
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