How many faces does a dodecahedron have whose vertices are $20$ and edges $30$ ?

12

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24

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20

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30

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Solution

The correct option is A $12$
Euler's polyhedron formula, $V - E + F = 2$
$V =$ number of vertices
$E =$ number of edges
$F =$ number of faces
So, $20 - 30 + F = 2$
$F - 10 = 2$
$F = 10 + 2$
$F = 12$
Number of faces $= 12$ .

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