1.

Can a polyhedron have 12 faces, 22 edges and 17 vertices?

Answer»

By Euler’s formula F + V -  E = 2 fora polyhedron.

Here F = 12, V = 17, E = 22 

F + V – E = 12 + 17 – 22 

= 29 – 22 

= 7 ≠ 2 

∴ The polyhedron cannot have 12 faces 22 edges and 17 vertices.


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