Editing Net (polyhedron) (section)

{{Short description|Edge-joined polygons which fold into a polyhedron}}
[[File:Dodecahedron flat.svg|thumb|A net of a [[regular dodecahedron]]]]
[[File:The 11 cubic nets.svg|thumb|The eleven nets of a cube]]

In [[geometry]], a '''net''' of a [[polyhedron]] is an arrangement of non-overlapping [[Edge (geometry)|edge]]-joined [[polygon]]s in the [[plane (geometry)|plane]] which can be folded (along edges) to become the [[face (geometry)|face]]s of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and [[solid geometry]] in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard.<ref>{{citation|first=Magnus J.|last=Wenninger|author-link=Magnus Wenninger|title=Polyhedron Models|publisher=Cambridge University Press|year=1971}}</ref>

An early instance of polyhedral nets appears in the works of [[Albrecht Dürer]], whose 1525 book ''A Course in the Art of Measurement with Compass and Ruler'' (''Unterweysung der Messung mit dem Zyrkel und Rychtscheyd '') included nets for the [[Platonic solid]]s and several of the [[Archimedean solid]]s.<ref>{{citation|first=Albrecht|last=Dürer|author-link=Albrecht Dürer|title=Unterweysung der Messung mit dem Zyrkel und Rychtscheyd|location=Nürnberg|year=1525|url=https://archive.org/stream/albrechtdrersun01peltgoog#page/n142/mode/2up|pages=139–152|publisher=München, Süddeutsche Monatsheft}}. English translation with commentary in {{citation|first=Walter L.|last=Strauss|title=The Painter's Manual|location=New York|year=1977}}</ref><ref>Schreiber, Fischer, and Sternath claim that, earlier than Dürer, [[Leonardo da Vinci]] drew several nets for [[Luca Pacioli]]'s ''[[Divina proportione]]'', including a net for the regular dodecahedron. However, these cannot be found in [https://archive.org/details/diuinaproportion00paci online copies of the 1509 first printed edition of this work] nor in the 1498 [https://www.e-codices.unifr.ch/it/list/one/bge/le0210 Geneva ms 210], so this claim should be regarded as unverified. See: {{citation
 | last1 = Schreiber | first1 = Peter
 | last2 = Fischer | first2 = Gisela | author2-link = Gisela Fischer
 | last3 = Sternath | first3 = Maria Luise
 | date = July 2008
 | issue = 4
 | journal = Archive for History of Exact Sciences
 | jstor = 41134285
 | pages = 457–467
 | title = New light on the rediscovery of the Archimedean solids during the Renaissance
 | volume = 62| doi = 10.1007/s00407-008-0024-z
 }}</ref> These constructions were first called nets in 1543 by [[Augustin Hirschvogel]].<ref>{{citation|first= Michael|last=Friedman|publisher=Birkhäuser|year=2018|title=A History of Folding in Mathematics: Mathematizing the Margins|title-link=A History of Folding in Mathematics|series=Science Networks. Historical Studies|volume=59|isbn=978-3-319-72486-7|doi=10.1007/978-3-319-72487-4|page=8}}</ref>