Can a polyhedron have 10 faces, 20 edges and 15 vertices - Maths - Visualising Solid Shapes

Question

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

Gopal Mohanty · 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