Look at the shapes given below and state which of these polyhedral using Euler’s formula are.

(a) Edge-9, vetrices:-6, face:-5

By using Euler’s formula

F + V = E + 2

⟹ 5 + 6 = 9 + 2

⟹ 11 = 11. Therefore it is a polyhedral.

(b) Edge-12, vetrices:-8, face:-6

By using Euler’s formula

⟹ F + V = E + 2

⟹ 6 + 8 = 12 + 2

⟹ 14 = 14.therfore it is a polyhedral.

(c) Edge-2, vertices:-0, face:-3

By using Euler’s formula

F + V = E + 2

⟹ 3 + 0 = 2 + 2

⟹ .Hence it is not possible. Therefore it is not a polyhedral.

(d) Edge-15, vetrices:-10, face:-7

By using Euler’s formula

F + V = E + 2

⟹ 7 + 10 = 15 + 2

⟹ 17 = 17

Therefore, it is a polyhedral.

(e) Edge-9, vertices:-6,face:-5

By using Euler’s formula

F + V = E + 2

⟹ 5 + 6 = 9 + 2

⟹ 11 = 11 therefore it is a polyhedral.

(f) Edge-2, vertices:-0, face:-3

By using Euler’s formula

F + V = E + 2

⟹ 3 + 0 = 2 + 2⟹

It is not possible. Therefore, it is not polyhedral.

(g) Edge-20, vertices:-11, face:-11

By using Euler’s formula

F + V = E + 2

⟹ 11 + 11 = 20 + 2

⟹ 22 = 22. Therefore, it is a polyhedral.

(h) Edge-16, vertices:-9,face:-9

By using Euler’s formula

F + V = E + 2

⟹ 9 + 9 = 16 + 2

⟹ 18 = 18. Therefore it is a polyhedral.

(i) Edge-18, vertices:-12, face:-8

By using Euler’s formula

F + V = E + 2

⟹ 8 + 12 = 18 + 2

⟹ 20 = 20. Therefore it is a polyhedral.

(j) Edge-12, vertices:-6,face:-8

By using Euler’s formula

F + V = E + 2

⟹ 8 + 6 = 12 + 2

⟹ 14 = 14. Therefore it is a polyhedral.

(k) Edge-0, vetrices:-1, face:-2

By using Euler’s formula

F + V = E + 2

⟹ 2 + 1 = 0 + 2

⟹ 32. It is not possible. Therefore it is not a polyhedral.

(l) Edge-24, vetrices:-16, face:-10

By using Euler’s formula

F + V = E + 2

⟹ 10 + 16 = 24 + 2

⟹ 26 = 26. Therefore it is a polyhedral.

(m) Edge-1, vetrices:-0, face:-1

By using Euler’s formula

F + V = E + 2

⟹ 1 + 0 = 1 + 2

⟹ 13.it is not possible. Therefore it is not a polyhedral.