The perigynium is a sheath covering the ovary/achene in Carex. The perigynium surrounding the achene looks like a flat bottle. It is wafer-thin.

1. Heads ellipsoid or nearly so; stigmas 2...2

1. Heads cylindric; stigmas 3...C. verrucosa

2. Perigynium 3-4 mm wide...C. vexans

2. Perigynium 1.5-2.5 mm wide...C. longii