question_answer

A dodecahedron is having 20 vertices an 30 edges. How many faces are there?

Answer:

Here:

Number of vertices (V) =20

Number of edges (E) =30

Let the number of faces =F

Then using Euler?s formula, we have

F+V=E+2                 ?..(1)

\[\therefore \]Substituting the values of V and E in(1) ,we get

F+20=30+2

\[\Rightarrow \]            F +20=32

\[\Rightarrow \]            F\[=32-20\]

\[\Rightarrow \]            F=12

Thus, the required number of faces=12.