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Why only five Platonic Solids?
Dodecahedron


Tetrahedron


Cube

Octahedron


Icosahedron

Platonic Solids 
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Platonic Solids
There are five so named because they were known at the time of Plato circa (427347 BC). These polyhedra are also called regular polyhedra because they are made up of faces
that are all the same
regular polygon.


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? Tetrahedron: Octahedron: Icosahedron: Cube: Dodecahedron: Note:
*) Regular means that the sides of the polygon are all the
same length. 
External Links:
Mathforum dr.math faq Regular Polyhedra
Mathworld: Platonic Solid
University of Utah: Platonic Solids
Mathsisfun: Platonic Solids
Dartmouth College: Platonic Solids Unit6
Science U: Solids
Wikipedia: Platonic Solids
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