Question

7. Using Euler's formula find the unknown.
Faces
?
5
20
Vertices
6
2
12
Edges
12
9
2
8. Can a polyhedron have 10 faces, 20 edges and 15 vertices?​

Answer 1

Step-by-step explanation:

F+V=E+2

F+6=12+2

F=8

F+V=E+2

5+V=9+2

V=6

F+V=E+2

20+12=E+2

E=30

8.By Euler's formula for a polyhedron, Vertices (V) - Edges (E) + Faces (F) =2

Here, Faces (F) = 10; Vertices (V) = 15 and Edges (E) = 20

Thus, 15 - 20 + 10 = 5, which does not satisfy the Euler's formula.

Hence, a polyhedron cannot have 10 faces, 20 edges and 15 vertices

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