Question 142837
notice that: 
Each solid has flat sides called {{{faces}}}. 
Each solid has {{{edges}}} to connect the faces. 
Each solid has {{{vertices }}}that connect the edges. 

There are {{{many}}} different {{{solid}}}{{{ shapes}}} that are {{{polyhedra}}}. You can examine the shapes and count the number of faces, edges, and vertices for each. 

There are {{{only}}}{{{ five}}} regular polyhedra. This means that there are only five solids in which
all of the faces are congruent regular polygons. 

These five regular polyhedra are called the {{{Platonic}}}{{{ Solids}}}. The Platonic Solids are: 
the {{{tetrahedron}}} which has 4 equilateral triangles as faces; 
the {{{hexahedron}}} which has 6 squares as faces; 
the {{{octahedron}}} which has 8 equilateral triangles as faces; 
the {{{dodecahedron}}} which has 12 equilateral pentagons as faces;
and the {{{icosahedron}}} which has 20 triangles as faces.

Euler characteristic: there is a relation among the number of edges {{{E}}}, vertices {{{V}}}, faces {{{F}}}
{{{x=V - E + F=2 }}} This result is known as {{{Euler's}}}{{{ formula}}}, and can be applied not only to polyhedra but also to embedded planar graphs.