Question
Can a polyhedron have $10$ faces, $20$ edges and $15$ vertices$?$
✓
Answer
No, because every polyhedron satisfies Euler's formula, given below: $F + V = E + 2$
Here, number of faces $F = 10$
Number of edges $E = 20$
Number of vertices $V = 15$
So, by Euler's formula: $LHS: 10 + 15 = 25$
$RHS: 20 + 2 = 22$, which is not true because $25\neq22$
Hence, Eulers formula is not satisfied and no polyhedron may be formed.
Here, number of faces $F = 10$
Number of edges $E = 20$
Number of vertices $V = 15$
So, by Euler's formula: $LHS: 10 + 15 = 25$
$RHS: 20 + 2 = 22$, which is not true because $25\neq22$
Hence, Eulers formula is not satisfied and no polyhedron may be formed.
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