question

tabulate the number of faces, edges and vertices for the following polyhedrons: (here ‘v’ stands for number of vertices, ‘f’ stands for number of faces and ‘e’ stands for number of edges).

 
 
 solid
 f
 v
 e
 f+v
 e+2
 
 
 
 
 cuboid
  
  
  
  
  
 
 
 triangular pyramid
  
  
  
  
  
 
 
 triangular prism
  
  
  
  
  
 
 
 pyramid with square base
  
  
  
  
  
 
 
 prism with square base
  
  
  
  
  
 
 

what do you infer from the last two columns? in each case, do you find
, i.e., ? this relationship is called euler’s formula.
in fact this formula is true for any polyhedron.

379