octagon

Etymology

octagon, that is, one in which the lengths of the sides are equal, and the angles are all 135°.]] From Latin octagōnon, octōgōnon (“octagon”), and from its etymon Ancient Greek ὀκτάγωνον (oktágōnon, “octagon”), probably from Koine Greek ὀκτάγωνος (oktágōnos, “having eight corners”) + -ον (-on, suffix forming nouns). ὀκτάγωνος is derived from ὀκτᾰ- (okta-, prefix meaning ‘eight’) (from ὀκτώ (oktṓ, “eight”), ultimately from Proto-Indo-European *oḱtṓw (“eight”)) + γωνία (gōnía, “angle; corner”) (probably ultimately from Proto-Indo-European *ǵónu (“knee”)); analysable as octa- + -gon. The English word is cognate with Middle French octogone (modern French octogone), Italian octagono (obsolete), ottagono, Spanish octágono, octógono. Sense 2 (“arena for mixed martial arts”) refers to its shape.

noun

1. (geometry, also attributively) A polygon with eight sides and eight angles.
   From the Circle deſcribe the Octagon, by taking half the Quadrant of the former for each Side of the latter. … [B]y conjoining theſe Points with ſtrait Lines agreeable to the Shape of the Octagon, the whole Work is completed. 1707, Andrea Pozzo, “The Ninety-second Fig. An Octangular Cupola.”, in John James, transl., Rules and Examples of Perspective Proper for Painters and Architects, etc. in English and Latin:[…], London: […] Benj[amin] Motte [Sr.],[…]; [s]old by John Sturt[…], →OCLC
   In like manner it is demonſtrated that one angle of a regular hexagon will be equal to one right angle, and one third part of one right angle; one angle of a regular octagon equal to one right angle and half a right angle; … 1752, Euclid, “[Additions to the Fourth Book.] Prop[osition] VII. Probl[em]. To Describe any Regular Polygon upon a Given Right Line, Admitting the Division of a Given Arch of a Circle into any Number of Equal Parts.”, in E[dmund] Stone, transl., Euclid’s Elements of Geometry, the First Six, the Eleventh and Twelfth Books;[…], London: […] Tho[mas] Payne,[…], →OCLC, book IV, pages 199–200
   Bismuth is the most common of all native metallic substances. It is generally found either in cubes or octagons, or of a dendritical form, or else in thin laminæ investing the ores of other metals, particularly those of cobalt. 1808, William Nicholson, “Ores of Bismuth”, in A Dictionary of Practical and Theoretical Chemistry,[…], London: […] Richard Phillips,[…], →OCLC, column 2
   The building [the Winter Garden conservatory, Kew Gardens] was to be of five parts—a centre, two small octagons, and two wings connected by the octagons with the centre. The centre and the two octagons were finished, and some expenditure must have been laid out on the wings, as the ground was dug out and foundations in concrete laid for the pillars. 1 June 1863, [Charles William] Selwyn, “Supply—Civil Service Estimates. Supply Considered in Committee.”, in Hansard’s Parliamentary Debates, […] (House of Commons), volume CLXXI, London: Published by Cornelius Buck, at the office for “Hansard’s Parliamentary Debates,”[…], →OCLC, columns 214–215
   China converted the hard octagons of the Turkoman rugs into circular scrolls or medallions, beautifying them meanwhile with floral character manifestly borrowed from the Persians and yet by no means Persian. 28 October 1922, Roy C. Bennett, “Rug Gift to National Press Club Typifies New China Industry”, in J[ohn] B[enjamin] Powell, editor, The Weekly Review, volume XXII, number 9, Shanghai: Millard Publishing Company, →OCLC, page 299, column 2
2. (martial arts) Often in the form Octagon: the arena for mixed martial arts.