gaudii
Gaudii is the genitive singular form of the Latin noun gaudium, meaning “joy” or “delight.” It is commonly encountered in Latin texts as part of a possessive or descriptive phrase, for example to indicate “of joy” or “relating to joy.”
Gaudium, the nominative singular, is a second-declension neuter noun. Its full paradigm is: singular gaudium (nom./acc.),
In usage, gaudii appears mainly in genitive constructions to convey relational meaning, such as gaudii causa
Etymologically, gaudii derives from gaudium, a noun denoting joy, with gaudere (“to rejoice”) as its related verb.
See also: gaudium, gaudere, Latin grammar on the second declension neuter nouns.