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..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
....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]
......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]
........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].
............ 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]
............ ..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