Question

Can a polyhedron have 10faces, 20 edges, and 15 vertices
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Answer 1

$\huge \sf{ \underline{ \underline{Question}}}$

Can a polyhedron have 10faces, 20 edges, and 15 vertices

$\huge \sf{ \underline{ \underline{Solution:- }}}$

By Euler's formula for a polyhedron, 

$\sf \: Vertices (V) - Edges (E) + Faces (F) =2$

Here,  

• Faces (F) = 10
• Vertices (V) = 15
• Edges (E) = 20 

$\sf \: Thus, 15 - 20 + 10 = 5,$

Which does not satisfy the Euler's formula. 

Hence, a polyhedron cannot have 10 faces, 20 edges and 15 vertices.