Definition of a polyhedron  
Polyhedra  
The elements of a polyhedron. Euler's polyhedral formula.  
The houses we live in, the room we are
in now, books, pieces of
furniture... almost everything has a polyhedral shape: we live
surrounded by polyhedra. Vertices
are the corner points, they are at the ends of the edges. Three or more
faces converge in each vertex. A polyhedron has two space regions, one is inside of it and the other one is outside of it. 

 What type
of polyhedron is it? How
many faces does this polyhedron have? How many
edges does it have? How many
vertices does it have?  Type each answer in the corresponding box and hit Enter. When you get a correct answer, write down the values in your notebook.  Click on Init to get a different polyhedron (prism or pyramid). Repeat the previous activity and elaborate a table like this one with the data from several polyhedra. 


 Observe the data in this table and find out the relation between the numbers in the two columns on the right.


The mathematician Euler proved the relation among the numbers of faces, the numbers of vertices and the numbers of edges of a non toroidal polyhedron. A non toroidal polyhedron is understood as the one that doesn't form a ring, neither do any of its faces or edges. Those polyhedra  as they satisfy Euler's formula  are called Eulerian. 
Eduardo Barbero Corral  
Spanish Ministry of Education , Social Afairs and Sport. Year 2007  
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