Because the Greek 3rd declension is quite closely parallel to its Latin 3rd declension counterpart, you will understand why nouns of this class may have bases that are not apparent from their nominative (vocabulary) forms—cf. rex, REG-is and nomen, NOMIN-is, where the Latin bases are capitalized. In Latin, the noun stem that precedes the -is ending of the genitive case is regularly used as the BASE for all derivative words. In Greek, where the 3rd declension genitive ending is -ος, this same situation usually prevails; see, for example, the noun ἀνηρ, ἀνδρ-ος (base andr-), “man”, which we met in §111. However, we’ll find an occasional 3rd declension Greek noun with a base that differs from its stem—e.g., ὑδωρ, ὑδατ-ος (base hydr-), “water”; and there will be others that have two alternative bases—e.g., γυνη, γυναικ-ος (base gyn- or gynaik-), “woman.” Here the best advice is to remember the combining form(s) and not worry too much about the original Greek word.
Chapter 18: The Greek Noun (Declension 3)