View source for Platonic solid

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<gallery perrow="2" caption="The Platonic Solids" widths="80px" heights="80px">
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File:Tetrahedron.svg|[[Tetrahedron]]

File:Hexahedron.svg|[[Cube]]
File:Octahedron.svg|[[Octahedron]]

File:POV-Ray-Dodecahedron.svg|[[Dodecahedron]]
File:Icosahedron.svg|[[Icosahedron]]
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</div>
A '''Platonic solid''' is a kind of [[polyhedron]] (a [[three-dimensional]] [[shape]]). It has the following traits:

* Each of their faces is built from the same type of [[polygon]]s.
* All the edges are the same, and all of them join two faces at the same angle.
* There are the same polygons meeting at every [[corner]] of the shape.
* The shape is convex, meaning the faces do not go through each other (intersecting), or span the same range (coplanar).

==The Platonic solids==
The following Platonic solids exist; there are only 5:

*Triangular [[Pyramid (geometry)|pyramid]], or ''[[Tetrahedron]]'', has 4 sides, is made of [[triangle]]s, and is the simplest kind of polyhedron.
*[[Cube]], or ''Hexahedron'', has 6 sides, and is made of [[Square (geometry)|squares]]. It is a kind of [[Prism (geometry)|prism]].
*[[Octahedron]], has 8 sides, and is made of triangles. It is a kind of [[antiprism]].
*[[Dodecahedron]], has 12 sides, and is made of [[pentagon]]s. It has the most vertices.
*[[Icosahedron]], has 20 sides, and is made of triangles. It has the most faces.

==Uses==
[[Image:BluePlatonicDice.jpg|thumb|left|The Platonic Solids are often used as dice in role-playing games.]]
There are a lot of uses for Platonic solids, but some of the main reasons are:the shapes are often used to make [[dice]], because dice of these shapes can be made fair. 6-sided dice are very common, but the other numbers are commonly used in [[role-playing game]]s. Such dice are commonly referred to as D followed by the number of faces (d8, d20 etc.).

The tetrahedron (4 sided), cube (6 sided), and octahedron (8 sided), are found naturally in [[crystal]] structures. The dodecahedron (12 sides) is combinatorially identical to the [[pyritohedron]] (in that both have twelve pentagonal faces), which is one of the possible crystal structures of [[pyrite]]. However, the pyritohedron is not a regular dodecahedron, but rather has the same symmetry as the cube.

In [[meteorology]] and [[climatology]], global numerical models of atmospheric flow are of increasing interest which use grids that are based on an icosahedron (20 sides,refined by [[triangulation]]) instead of the more commonly used [[longitude]]/[[latitude]] grid. This has the advantage of better spatial resolution without [[singularities]] (i.e. the [[poles]]) at the expense of somewhat greater numerical difficulty.

Geometry of [[space frame]]s is often based on Platonic solids.

== Other websites ==
*[http://www.software3d.com/Stella.html Stella: Polyhedron Navigator] Tool for exploring polyhedra
*[http://www.korthalsaltes.com/ Paper Models of Polyhedra] Many links
*[http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra]
*[http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] The Encyclopedia o  Polyhedra
*[http://www.lsbu.ac.uk/water/platonic.html London South Bank University] Water structure and behavior
*[http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII13.html Book XIII] of Euclid's ''Elements''.
*[http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D Polyhedra] {{Webarchive|url=https://web.archive.org/web/20050403235101/http://ibiblio.org/e-notes/3Dapp/Convex.htm |date=2005-04-03 }} in Java


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[[Category:Platonic solids| ]]