Paraphysis

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Paraphyses in the antheridia and archegonia stands of Phascum cuspidatum
Paraphysis of Caloplaca holocarpa (Hoffm. Ex Ach.) Calf in potassium hydroxide

As paraphyses you have long called sterile organs between the reproductive organs of mosses and fungi are.

The sac fungi ( ascomycetes ) they are between the Asci . Together with the asci, they form the hymenium (fruit layer) of the fungus.

The multicellular sap hairs that stand between the male ( Antheridium ) and female ( Archegonium ) reproductive organs in the deciduous mosses are also called "paraphyses".