Editing Polyhedron (section)

===Ancient Greece===
{{multiple image
 | align = right |total_width=500
 | image1 = Kepler Hexahedron Earth.jpg |width1=290|height1=304
 | image2 = Kepler Icosahedron Water.jpg |width2=306|height2=328
 | image3 = Kepler Octahedron Air.jpg |width3=328|height3=334
 | image4 = Kepler Tetrahedron Fire.jpg |width4=367|height4=328
 | image5 = Kepler Dodecahedron Universe.jpg |width5=330|height5=332
 | footer = five elements in each Platonic solids, but the assignment drawing was by Kepler's ''Harmonices Mundi''
}}
Ancient Greek mathematicians discovered and studied the [[Regular polyhedron#History|convex regular polyhedra]], which came to be known as the [[Platonic solid]]s. Their first written description is in the ''[[Timaeus (dialogue)|Timaeus]]'' of [[Plato]] (circa 360 BC), which associates four of them with the [[four elements]] and the fifth to the overall shape of the universe. A more mathematical treatment of these five polyhedra was written soon after in the ''[[Euclid's Elements|Elements]]'' of [[Euclid]]. An early commentator on Euclid (possibly [[Geminus]]) writes that the attribution of these shapes to Plato is incorrect: [[Pythagoras]] knew the [[tetrahedron]], [[cube]], and [[dodecahedron]], and [[Theaetetus (mathematician)|Theaetetus]] (circa 417 BC) discovered the other two, the [[octahedron]] and [[icosahedron]].<ref>{{citation | last = Eves | first = Howard | date = January 1969 | department = Historically Speaking | doi = 10.5951/mt.62.1.0042 | issue = 1 | journal = The Mathematics Teacher | jstor = 27958041 | pages = 42–44 | title = A geometry capsule concerning the five platonic solids | volume = 62}}</ref> Later, [[Archimedes]] expanded his study to the [[Uniform polyhedron|convex uniform polyhedra]] which now bear his name. His original work is lost and his solids come down to us through [[Pappus of Alexandria|Pappus]].<ref>{{citation | last = Field | first = J. V. | author-link = Judith V. Field | doi = 10.1007/BF00374595 | issue = 3–4 | journal = Archive for History of Exact Sciences | jstor = 41134110 | mr = 1457069 | pages = 241–289 | title = Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler | volume = 50 | year = 1997| s2cid = 118516740 }}</ref>