Editing Truncated icosahedron (section)

== Appearance ==
[[File:Comparison of truncated icosahedron and soccer ball.png|thumb|upright=1.1|The truncated icosahedron (left) compared with an [[Ball (association football)|association football]]]]
The balls used in [[Football (association football)|association football]] and [[Team handball#Ball|team handball]] are perhaps the best-known example of a [[spherical polyhedron]] analog to the truncated icosahedron, found in everyday life.{{r|kotschick}} The ball comprises the same pattern of regular pentagons and regular hexagons, each of which is painted in black and white respectively; still, its shape is more spherical. It was introduced by [[Adidas]], which debuted the [[Adidas Telstar|Telstar ball]] during [[1970 FIFA World Cup|World Cup in 1970]].{{r|hh}} However, it was superseded in [[2006 World Cup|2006]].{{r|pmtsgsd}}

[[File:Buckminsterfullerene Model in Red Beads.jpg|thumb|left|upright=0.8|The [[buckminsterfullerene]] molecule]]
[[Geodesic dome]]s are typically based on triangular facetings of this geometry with example structures found across the world, popularized by [[Buckminster Fuller]]. An example can be found in the model of a [[buckminsterfullerene]], a truncated icosahedron-shaped geodesic dome [[allotrope]] of elemental carbon discovered in 1985.{{r|katz-2006}} In other engineering and science applications, its shape was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in both [[the gadget]] and [[Fat Man]] [[atomic bomb]]s.{{r|rhodes}} Its structure can also be found in the [[protein]] of [[clathrin]].{{r|kostant}}

[[File:Piero della Francesca - Libellus de quinque corporibus regularibus - p52b (cropped).jpg|thumb|upright=1.1|[[Piero della Francesca]]'s image of a truncated icosahedron from his book ''[[De quinque corporibus regularibus]]'']]
The truncated icosahedron was known to [[Archimedes]], who classified the 13 Archimedean solids in a lost work. All that is now known of his work on these shapes comes from [[Pappus of Alexandria]], who merely lists the numbers of faces for each: 12 pentagons and 20 hexagons, in the case of the truncated icosahedron. The first known image and complete description of a truncated icosahedron are from a rediscovery by [[Piero della Francesca]], in his 15th-century book ''[[De quinque corporibus regularibus]]'', which included five of the Archimedean solids (the five truncations of the regular polyhedra).{{r|katz-2011}} The same shape was depicted by [[Leonardo da Vinci]], in his illustrations for [[Luca Pacioli]]'s plagiarism of della Francesca's book in 1509. Although [[Albrecht Dürer]] omitted this shape from the other Archimedean solids listed in his 1525 book on polyhedra, ''Underweysung der Messung'', a description of it was found in his posthumous papers, published in 1538. [[Johannes Kepler]] later rediscovered the complete list of the 13 Archimedean solids, including the truncated icosahedron, and included them in his 1609 book, ''[[Harmonices Mundi]]''.{{r|field}}