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

Question

Philoid · Accepted Answer

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