Editing Polygon (section)

==History==
[[File:Fotothek df tg 0003352 Geometrie ^ Dreieck ^ Viereck ^ Vieleck ^ Winkel.jpg|thumb|Historical image of polygons (1699)]]
Polygons have been known since ancient times. The [[regular polygon]]s were known to the ancient Greeks, with the [[pentagram]], a non-convex regular polygon ([[star polygon]]), appearing as early as the 7th century B.C. on a [[krater]] by [[Aristophanes (vase painter)|Aristophanes]], found at [[Caere]] and now in the [[Capitoline Museum]].<ref>{{citation|title=A History of Greek Mathematics, Volume 1|first=Sir Thomas Little|last=Heath|author-link=Thomas Little Heath|publisher=Courier Dover Publications|year=1981|isbn=978-0-486-24073-2|page=162|url=https://books.google.com/books?id=drnY3Vjix3kC&pg=PA162}} Reprint of original 1921 publication with corrected errata. Heath uses the Latinized spelling "Aristophonus" for the vase painter's name.</ref><ref>[http://en.museicapitolini.org/collezioni/percorsi_per_sale/museo_del_palazzo_dei_conservatori/sale_castellani/cratere_con_l_accecamento_di_polifemo_e_battaglia_navale Cratere with the blinding of Polyphemus and a naval battle] {{webarchive|url=https://web.archive.org/web/20131112080845/http://en.museicapitolini.org/collezioni/percorsi_per_sale/museo_del_palazzo_dei_conservatori/sale_castellani/cratere_con_l_accecamento_di_polifemo_e_battaglia_navale |date=2013-11-12 }}, Castellani Halls, Capitoline Museum, accessed 2013-11-11. Two pentagrams are visible near the center of the image,</ref>

The first known systematic study of non-convex polygons in general was made by [[Thomas Bradwardine]] in the 14th century.<ref>Coxeter, H.S.M.; ''Regular Polytopes'', 3rd Edn, Dover (pbk), 1973, p. 114</ref>

In 1952, [[Geoffrey Colin Shephard]] generalized the idea of polygons to the complex plane, where each [[real number|real]] dimension is accompanied by an [[imaginary number|imaginary]] one, to create [[complex polytope|complex polygons]].<ref>Shephard, G.C.; "Regular complex polytopes", ''Proc. London Math. Soc.'' Series 3 Volume 2, 1952, pp 82–97</ref>