Can a polyhedron have 8 faces, 26 edges and 16 vertices?

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Solution

Number of faces = 8
Number of vertices = 16
Number of edges = 26
Using Euler's formula
$F + V - E \Rightarrow 8 + 16 - 26 \neq - 2 \Rightarrow - 2 \neq 2$
No, a polyhedron cannot have 8 faces, 26 edges and 16 vertices.

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