The outer protective layer or outer skin of a fungal fruiting body, especially in puffballs and similar fungi.
From Greek 'exo-' (outside) and 'peridium' (the envelope that contains spores in fungi). This botanical term specifically names the outermost of potentially multiple layers that fungi use to protect their spores.
When you look at a puffball mushroom, the thin papery outer layer you see and might peel off is the exoperidium—and if you cut one open, you might find there's another layer underneath called the endoperidium, creating a Russian-nesting-doll structure for spore protection.
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