Question

Can a polyhedron have 20 Faces, 30 Edges and 12 Vertices? Prove by Euler's formula.​

Answer 1

Answer:

According to the formula given by Euler. Therefore, there are 30 edges of a polyhedron having 20 faces and 12 vertices.

Step-by-step explanation:

I hope it will help you army

Answer 2

Answer:

Yes ,a polyhedron have 20 face , 30 edges and 12 vertices .

Step-by-step explanation:

Explanation:

Given ,  vertices = 12 , face = 20 and Edges = 30 .

• The relationship between the faces and vertices of polyhedron is determined using Euler's formula in geometry. Euler's formula is also used in trigonometry to trace the unit circle.

• F is the number of faces, V is the number of vertices, and E is the number of edges.
• This equation is represented as F + V = E + 2.

Step 1:

From the question we have , face = 20 , edges = 30 and vertices = 12

Now , from the Euler's formula ,

F + V = E + 2

Put the given value in the above formula we get

⇒20 + 12 = 30 + 2

⇒32 = 32

LHS = RHS

This means that it satisfy the Euler's formula .

Final answer:

Hence , yes a polyhedron have 20 face , 30 edges and 12 vertices .

#SPJ3