1530s, in architecture and masonry, "cornerstone, external solid angle," a variant spelling of coin (n.); in early use also in other senses of that word, including "a wedge, wedge-like piece of stone, wood, etc."
in carpentry, "a joint at a 45 degree angle," 1670s, of uncertain origin, perhaps from mitre, via notion of joining of the two peaks of the folded cap. As a verb, to make or join with a miter-joint," from 1731. Related: Mitered. Miter-box is attested from 1670s.
also nooky, "sexual activity," slang, generally used by men, by 1928, perhaps from Dutch neuken "to copulate with," but it is not impossible to connect it to nook (n.) on the notion of "an angle" or "a secluded spot." The adjective nooky "full of nooks, nook-like" is recorded from 1813.
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]
