Using Euler's formula find the unknown: Faces ? 5 20 Vertices 6 ?… - Vidyadip

Question

Using Euler's formula find the unknown:

Faces	?	5	20
Vertices	6	?	12
Edges	12	9	?

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Answer

We know that the Euler's formula is: F + V = E + 2

The number of vertices V is 6 and the number of edges E is 12.

Using Euler's formula:

F + 6 = 12 + 2

F + 6 = 14

F = 14 - 6

F = 8

So, the number of faces in this polyhedron is 8.

Faces, F = 5

Edges, E = 9

We have to find the number of vertices.

Putting these values in Euler's formula:

5 + V = 9+ 25 + V = 11

V = 11 - 5

V = 6

So, the number of vertices in this polyhedron is 6.

Number of faces F = 20

Number of vertices V = 12

Using Euler's formula:

20 + 12 = E + 2

32 = E + 2

E + 2 = 32

E = 32 - 2

E = 30

So, the number of edges in this polyhedron is 30.

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