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# Pictures of Platonic Solids

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Why only five Platonic Solids?

## Icosahedron Number of faces: 20 Number of edges: 30 Number of vertices: 12

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Platonic Solids
There are five so named because they were known at the time of Plato circa (427-347 BC).  These polyhedra are also called regular polyhedra because they are made up of faces that are all the same regular polygon.

 Why only five Platonic Solids A Platonic solid is a polyhedron all of whose faces are congruent regular convex polygons*, and where the same number of faces meet at every vertex. The Greeks recognized that there are only five platonic solids. But why is this so? The key observation is that the interior angles of the polygons meeting at a vertex of a polyhedron add to less than 360 degrees. Tetrahedron: Three triangels at a vertex: 3*60 = 180 degrees Octahedron: Four triangles at a vertex: 4*60 = 240 degrees Icosahedron: Five triangles at a vertex: 5*60 = 300 degrees Cube: Three squares at a vertex: 3*90 = 270 degrees Dodecahedron: Three pentagons at a vertex: 3*108 = 324 degrees Note:   Six triangles: 6*60 = 360 degrees   Four squares: 4*90 = 360 degrees   Four pentagons: 4*108 = 432 degrees   Three hexagons: 3*120 = 360 degrees So there are only five Platonic Solids!     *) Regular means that the sides of the polygon are all the same length. Congruent means that the polygons are all the same size and shape.

Platonic Solids:

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