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

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asked Jan 10, 2018 in Mathematics by Golu (37,045 points) ● 19 ● 145 ● 416

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

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answered Jan 10, 2018 by Annu Priya (18,055 points) ● 24 ● 45 ● 83

If F = 10, V = 15 and E = 20.
Then, we know Using Euler’s formula, F + V – E = 2
L.H.S. = F + V – E
= 10 + 15 – 20
= 25 – 20
= 5
R.H.S. = 2
L.H.S. ≠ R.H.S.
Therefore, it does not follow Euler’s formula.

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