Question

can a polyhedron have 8 faces,18 edges and 15 vertices?give reason.

Answer 1

Number of faces = F = 8

Number of edges = E = 18

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 = 8 + 15 − 18 = 23 − 18 = 5 ≠ 2

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