Question

can a polyhedron have 10 faces 20 edges and 15 vertices ? Explain​

Answer 1

Possibility of this bring a polyhedron can be proved by Euler's formula, i.e

F+V-E=2

F=10 V=15 E=20

=10+15-20

=25-20

=5$\ne$25

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=2 Euler;s formula can't be proved. Hence,a polyhedron can not have 10 faces,20 edges and 15 vertices

Answer 2

By Euler's formal for a

Polyhedron, vertical (v) - Edges (E) +Faces (F) =2

Hence, faces (F) =10; vertices (V) =15 and Edges (E) =20

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

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Thanks for the point

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