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
F + V = E + 2, i.e., F + V – E = 2? This relationship is called Euler’s formula.
In fact this formula is true for any polyhedron.

Answers (1)

 

 

Solid F V E F+V E+2
Cuboid 6 8 12 14 14
Triangular pyramid 4 4 6 8 8
Triangular prism 5 6 9 11 11
Pyramid with square base 5 5 8 10 10
Prism with square base 6 8 12 14 14

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