can a polyhedron have 12 faces,15 edges , 20 vertices. explain

No.

Because according to Euler's Theorm

Faces + Vertices - edges = 2

But here, faces = 12 , vertices = 15 , edges = 20

so, 12 + 15 - 20 = 7 that is not equal to 2.

This equation is not satisfying.

Hence it is not possible to have such polyhedron.

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