Can a Polyhedron Have 10 Faces, 20 Edges and 15 Vertices?

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

Number of faces = F = 10

Number of edges = E = 20

Number of vertices = V = 15

Any polyhedron satisfies Euler’s Formula, according to which, F + V − E = 2

For the given polygon,

F + V − E = 10 + 15 − 20 = 25 − 20 = 5 ≠ 2

Since Euler’s formula is not satisfied, such a polyhedron is not possible.

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