Question

Verify Euler's formula for each of the following polyhedrons:

Answer 1

(i) In this polyhedron,

Number of face (F) =7

Number of edges (E) =15

Number of vertices (V) =10

According Euler's formula,

F+V=E+2

$\Rightarrow 7+10=15+2\Rightarrow 17=17$

Which is true

(ii) In this polyhedron,

Number of face (F) =9

Number of edges (E) =16

Number of vertices (V) =9

According Euler's formula,

F+V=E+2

$\Rightarrow 9+9=16+2\Rightarrow 18=18$

Which is true

(iii) In this polyhedron, Number of face (F) =9

Number of edges (E) =18

Number of vertices (V) =11

According Euler's formula,

F+V=E+2

$\Rightarrow 9+11=18+2\Rightarrow 20=20$

Which is true

(iv) In this polyhedron,

Number of face (F) =5

Number of edges (E) =8

Number of vertices (V) =5

According Euler's formula,

F+V=E+2

$\Rightarrow 5+5=8+2\Rightarrow 10=10$

Which is true

(v) In the given polyhedron,

Number of face (F) =9

Number of edges (E) =16

Number of vertices (V) =9

According Euler's formula,

F+V=E+2

$\Rightarrow 9+9=16+2\Rightarrow 18=18$

Which is true