Question

Q – 4 Find the solution using Euler’s formula. (06) (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:

Step-by-step explanation:

Euler’s formula for any polyhedrons:

⇒F+V-E=2.

Given , F=a and V=6 and E=6.

According to formula;

⇒a+6-6=2.

⇒a+0=2.

⇒a=2.

And ,

Yes, polyhedrons also have 20 Faces , 30 Edges and 12 Vertices.

Euler’s formula for any polyhedrons:

⇒F+V-E=2.

Given , F=20 and V=12 and E=a.

According to formula;

⇒20+12-a=2.

⇒32-a=2.

⇒a=32-2.

⇒a=30.