The Phrygian cap was typically worn by the inhabitants of Phrygia, in the Anatolian peninsula, and is commonly mistaken for being a Pileus.
Pileus length x width x height (thickness) can range from 1-9 cm (l) x 1-7 cm (w) x 0.2-2 cm (h).
In describing a pileus or "cap" of a mushroom, it refers to radiating stripes or ribs, as in Tricholoma virgatum.