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

Solution

Since every polyhedron satisfies Euler’s formula, therefore checking if polyhedron can have 10 faces, 20 edges and 15 vertices.
No. of Faces (F) = 10
No. of Vertices (V) = 15
No. of Edges (E) = 20
By Using Euler’s formula: F + V – E = 2 and Substituting the values, we get
⇒ 10 + 15 – 20 = 2
⇒ -5 = 2
As Euler’s formula is not satisfied, therefore polyhedron cannot have 10 faces, 20 edges and 15 vertices.