Editing Platonic solid (section)

== In nature and technology ==
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[[Image:Circogoniaicosahedra ekw.jpg|frame|''Circogonia icosahedra'', a species of [[radiolaria]], shaped like a [[regular icosahedron]].]]

The tetrahedron, cube, and octahedron all occur naturally in [[crystal structure]]s. These by no means exhaust the numbers of possible forms of crystals. However, neither the regular icosahedron nor the regular dodecahedron are amongst them. One of the forms, called the [[pyritohedron]] (named for the group of [[pyrite|minerals]] of which it is typical) has twelve pentagonal faces, arranged in the same pattern as the faces of the regular dodecahedron. The faces of the pyritohedron are, however, not regular, so the pyritohedron is also not regular. [[Allotropes of boron]] and many [[crystal structure of boron-rich metal borides|boron compounds]], such as [[boron carbide]], include discrete B<sub>12</sub> icosahedra within their crystal structures. [[Carborane acid]]s also have molecular structures approximating regular icosahedra.

In the early 20th century, [[Ernst Haeckel]] described a number of species of [[Radiolaria]], some of whose skeletons are shaped like various regular polyhedra. Examples include ''Circoporus octahedrus'', ''Circogonia icosahedra'', ''Lithocubus geometricus'' and ''Circorrhegma dodecahedra''. The shapes of these creatures should be obvious from their names.<ref>[[Ernst Haeckel|Haeckel, Ernst]], E. (1904). ''Kunstformen der Natur''. Available as Haeckel, E. (1998); ''[https://web.archive.org/web/20090627082453/http://caliban.mpiz-koeln.mpg.de/~stueber/haeckel/kunstformen/natur.html Art forms in nature]'', Prestel USA. {{isbn|3-7913-1990-6}}.</ref>

Many [[virus]]es, such as the [[herpes]]<ref>{{cite journal |title= Why large icosahedral viruses need scaffolding proteins |author=Siyu Li, [[Polly Roy]], Alex Travesset, and [[Roya Zandi]] |date= October 2018 |journal=Proceedings of the National Academy of Sciences |volume= 115 |issue= 43 |pages= 10971–10976 |doi= 10.1073/pnas.1807706115 |pmid= 30301797 |pmc= 6205497 |bibcode= 2018PNAS..11510971L |quote=|doi-access= free }}</ref> virus, have the shape of a regular icosahedron. Viral structures are built of repeated identical [[protein]] subunits and the icosahedron is the easiest shape to assemble using these subunits. A regular polyhedron is used because it can be built from a single basic unit protein used over and over again; this saves space in the viral [[genome]].

In [[meteorology]] and [[climatology]], global numerical models of atmospheric flow are of increasing interest which employ [[geodesic grid]]s that are based on an icosahedron (refined by [[triangulation]]) instead of the more commonly used [[longitude]]/[[latitude]] grid. This has the advantage of evenly distributed spatial resolution without [[Mathematical singularity|singularities]] (i.e. the poles) at the expense of somewhat greater numerical difficulty.

Geometry of [[space frame]]s is often based on platonic solids. In the MERO system, Platonic solids are used for naming convention of various space frame configurations. For example, {{sfrac|1|2}}O+T refers to a configuration made of one half of octahedron and a tetrahedron.

Several [[Platonic hydrocarbons]] have been synthesised, including [[cubane]] and [[dodecahedrane]] and not [[tetrahedrane]].

<gallery>
Image:Tetrahedrane-3D-balls.png |[[Tetrahedrane]]
Image:Cubane-3D-balls.png |[[Cubane]]
Image:Dodecahedrane-3D-balls.png|[[Dodecahedrane]]
</gallery>

=== Liquid crystals with symmetries of Platonic solids ===
For the intermediate material phase called [[liquid crystal]]s, the existence of such symmetries was first proposed in 1981 by [[Hagen Kleinert|H. Kleinert]] and K. Maki.<ref>Kleinert and Maki (1981)</ref><ref>{{cite web |title=''The liquid-crystalline blue phases'' (1989). by Tamar Seideman, Reports on Progress in Physics, Volume 53, Number 6 |url=http://chemgroups.northwestern.edu/seideman/Publications/The%20liquid-crystalline%20blue%20phases.pdf}}</ref>
In aluminum the icosahedral structure was discovered three years after this by [[Dan Shechtman]], which earned him the [[Nobel Prize in Chemistry]] in 2011.