Question

Q– 4 Find the solution using Euler’s formula.
(1) If the number of vertices (V) is 6 and Edges (E) is 12 in a polyhedron, then find its number of
Faces(F).
(2) Can a polyhedron have 20 Faces, 30 Edges and 12 Vertices? Prove by Euler’s formula.​

Answer 1

Answer:

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Step-by-step explanation:

Solution 7: (i) Faces-?,vertices-6,edges-12

Euler's formula: F+V–E=2

F+6–12=2

F=2+12–6=8

F=8

(ii) Faces-5,vertices-?,edges-9

Euler's formula: F+V–E=2

5+V–9=2

V=2+9–5=6

V= 6

(iii) Faces-20,vertices-12,edges-?

Euler's formula: F+v–E=2

20+12–E=2 ,

E=20+12–2

E=30