nonagon n.

"the cardinal number one more than eight or one less than ten; the number which is one more than eight;" Middle English nīn, from Old English nigen, from Proto-Germanic *newun (source also of Old Saxon nigun, Old Frisian niugun, Old Norse niu, Swedish nio, Middle Dutch neghen, Dutch negen, Old High German niun, German neun, Gothic niun "nine").

This is from PIE root *newn "nine" (source also of Sanskrit nava, Avestan nava, Greek ennea (with unetymological initial e-), Albanian nende, Latin novem (with change of -n- to -m- by analogy of septem, decem), Lithuanian devyni, Old Church Slavonic deveti (the Balto-Slavic forms by dissimilation of -n- to -d-), Old Irish noin, Welsh naw).

As "a symbol representing the number nine," late 14c. The proverbial nine lives of a cat are attested from 17c.  Nine-to-five "the average workday" is attested from 1935. Nine days (or nights) has been proverbial since mid-14c. for the time which a wonder or novelty holds attention; the expression nine days' wonder is from 1590s. The Nine "the Muses" is from c. 1600. Also see nines.

1560s, "plane figure with five angles and five sides," from French pentagone (13c.) or directly from Late Latin pentagonum "pentagon," from Greek pentagōnon, a noun use of the neuter of the adjective pentagōnos "five-angled," from pente "five" (from PIE root *penkwe- "five") + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). The U.S. military headquarters known as the Pentagon was completed in 1942, and so called for its shape; used allusively for "U.S. military leadership" from 1945; Pentagonese "U.S. official military jargon" is by 1951. Related: Pentagonal.

In nature, pentagonal symmetry is rare in inanimate forms. Packed soap bubbles seem to strive for it but never quite succeed, and there are no mineral crystals with true pentagonal structures. But pentagonal geometry is basic to many living things, from roses and forget-me-nots to sea urchins and starfish. [Robert Bringhurst, "The Elements of Typographic Style," 1992]