Q. 72

# Check whether a polyhedron can have V = 12, E = 6 and F = 8.

Answer :

according to the data given in question

Vertices (V) = 12, Face(F) = 8 and Edge(E) = 6

By Euler’s formula we know that

Face + Vertices = Edge + 2

So,Face + vertices = 8 + 12 = 20

and Edge + 2 = 6 + 2 = 8

⟹ 208

Therefore Face + VerticesEdge + 2

So, the polyhedron is not possible for the above data

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