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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 polygons.
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, or Tetrahedron, has 4 sides, is made of triangles, and is the simplest kind of polyhedron.
Cube, or Hexahedron, has 6 sides, and is made of squares. It is a kind of prism.
Octahedron, has 8 sides, and is made of triangles. It is a kind of antiprism.
Dodecahedron, has 12 sides, and is made of pentagons. It has the most vertices.
Icosahedron, has 20 sides, and is made of triangles. It has the most faces.

Uses

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 games. 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 frames is often based on Platonic solids.

Other websites

Stella: Polyhedron Navigator Tool for exploring polyhedra
Paper Models of Polyhedra Many links
The Uniform Polyhedra
Virtual Reality Polyhedra The Encyclopedia o Polyhedra
London South Bank University Water structure and behavior
Book XIII of Euclid's Elements.
Interactive 3D Polyhedra Archived 2005-04-03 at the Wayback Machine in Java

This short article about mathematics can be made longer. You can help Wikipedia by adding to it.

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 </div>
-A '''platonic solid''' is a three dimensional [[shape]]. It has the following characteristics:
+A '''Platonic solid''' is a kind of [[polyhedron]] (a [[three-dimensional]] [[shape]]). It has the following traits:
-*Each face is built from the same type of [[polygon]]s
+* Each of their faces is built from the same type of [[polygon]]s.
-*There are the same number of polygons meeting at every corner of the shape.
+* 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 Platonic solids==
 The following Platonic solids exist; there are only 5:
-*[[Tetrahedron]], has 4 sides, is made of [[triangle]]s, and looks like a [[pyramid]].
+*Triangular [[Pyramid (geometry)|pyramid]], or ''[[Tetrahedron]]'', has 4 sides, is made of [[triangle]]s, and is the simplest kind of polyhedron.
-*[[Cube]], ''Hexahedron'', has 6 sides, and is made of [[square]]s.
+*[[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.
+*[[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.
+*[[Dodecahedron]], has 12 sides, and is made of [[pentagon]]s. It has the most vertices.
-*[[Isosahedron]], has 20 sides, and is made of triangles.
+*[[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.]]
-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.).
+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.
@@ Line 33: / Line 35: @@
 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.
+Geometry of [[space frame]]s is often based on Platonic solids.
 == Other websites ==
@@ Line 42: / Line 44: @@
 *[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] in Java
+*[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
-{{math-stub}}
-[[Category:Mathematics]]
+{{math-stub}}
-[[az:Düzgün çoxüzlülər]]
-[[bg:Платоново тяло]]
+[[Category:Platonic solids| ]]
-[[cs:Platónské těleso]]
-[[da:Platonisk legeme]]
-[[de:Platonischer Körper]]
-[[en:Platonic solid]]
-[[es:Sólidos platónicos]]
-[[eo:Platona solido]]
-[[eu:Solido platoniko]]
-[[fr:Solide de Platon]]
-[[gl:Sólido platónico]]
-[[ko:정다면체]]
-[[it:Solido platonico]]
-[[he:פאון משוכלל]]
-[[la:Corpus Platonicum]]
-[[hu:Szabályos test]]
-[[nl:Regelmatig veelvlak]]
-[[ja:正多面体]]
-[[no:Platonsk legeme]]
-[[pms:Sòlid ëd Platon]]
-[[pl:Wielościan foremny]]
-[[pt:Sólido platónico]]
-[[ro:Poliedru regulat]]
-[[ru:Правильный многогранник]]
-[[sl:Platonsko telo]]
-[[sr:Правилни полиедри]]
-[[fi:Platonin kappale]]
-[[sv:Platonska kroppar]]
-[[th:ทรงตันเพลโต]]
-[[uk:Правильний багатогранник]]
-[[ur:Platonic solid]]
-[[zh-classical:正多面體]]
-[[zh:正多面體]]