pi·le·us 
(pīlē-əs)
(pīlē-əs)n. pl. pi·le·i (-lē-ī′)
1. Botany The umbrellalike fruiting structure forming the top of a stalked fleshy fungus, such as a mushroom; the cap.
2. A brimless round skullcap worn by ancient Romans.
3. See caul.
[New Latin pīleus, from Latin, cap.]